Answer:
Phoebe's age = 24 years.
Step-by-step explanation:
Given:
Highest Common Factor and Lowest Common Multiple of the ages are 3 and 168 respectively.
Phoebe is 3 years older than Jody.
To find:
The age of Phoebe = ?
Solution:
Here, We have two numbers whose
HCF = 3 and
LCM = 168
Let the age of Phoebe = P years and
Let the age of Jody = J years
As per given statement:
[tex]P = J + 3 ...... (1)[/tex]
Let us learn about the property of LCM and HCF of two numbers.
The product of LCM and HCF of two numbers is equal to the product of the two numbers themselves.
LCM [tex]\times[/tex] HCF = P [tex]\times[/tex] J
[tex]\Rightarrow P\times J = 3 \times 168 \\\Rightarrow P\times J = 504[/tex]
Putting the value of P from equation (1):
[tex]\Rightarrow (J+3)\times J = 504\\\Rightarrow J^2+3J-504 = 0\\\Rightarrow J^2+24J-21J-504 = 0\\\Rightarrow J(J+24) - 21(J+24) = 0\\\Rightarrow (J - 21)(J+24) = 0\\\Rightarrow J = 21, -24[/tex]
Negative value for age is not possible So, Jody's age = 21 years
Using equation (1):
Phoebe's age = 21 + 3 = 24 years.
The number that, when increased by 30% equals 78
Answer:
60
Step-by-step explanation:
x + 0.30x = 78
1.30x = 78
x = 60
Answer:
The answer is 60.
Step-by-step explanation:
here, let another number be x.
according to the question the number when increased by 30% will be 78. so,
x+ 30% of x =78
now, x+ 30/100×x =78
or, x+0.3x=78
or, 1.3x=78
Therefore the another number is 60.
Hope it helps...
Forty percent of all undergraduates at a university are chemistry majors. In a random sample of six students, find the probability that exactly two are chemistry majors. 12. The probability that exactly two are chemistry majors is Type an integer or a decimal. Round to four decimal places as needed.)
Answer:
0.3110
Step-by-step explanation:
This is a binomial distribution with probability of success (being a chemistry major) p = 0.40.
The general formula for a binomial distribution is:
[tex]P(x=k)=\frac{n!}{(n-k)!k!}*p^k*(1-p)^{n-k}[/tex]
Where n is the sample size and k is the desired number of successes.
The probability of k=2 in a sample of n =6 is:
[tex]P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2} \\P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2}\\P(x=2)=3*5*0.4^2*0.6^4\\P(x=2)=0.3110[/tex]
The probability is 0.3110
There are two pennies lying flat on a table. One of the pennies is fixed to the table, while the other one is being rolled around the fixed one staying tangent to it all the way. How many spins will it make by the time it returns to the starting point ?
Answer:
well if you want my answer even though it could not be right so dont get mad at me if i am wrong but i think that it is all mostly based on how far they are from each other the further it is the more it will roll the closer it is the less it it will roll
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
rolling it shows its circumference and the other pennine has the ame circumference
[tex]x+7-4(x+1)=-10[/tex]
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 13/3, 4 1/3, or 4.3
▹ Step-by-Step Explanation
x + 7 - 4(x + 1) = -10
x + 7 - 4x - 4 = -10
-3x + 7 - 4 = -10
-3x + 3 = -10
-3x = -10 - 3
-3x = -13
x = 13/3, 4 1/3, or 4.3
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
x = 13/3
Step-by-step explanation:
x + 7 - 4(x + 1) = -10
x + 7 - 4x - 4 = -10
-3x + 3 = -10
-3x = -13
x = -13/(-3)
x = 13/3
What is the product of 3x(x^2+4)?
0 + 3x + 4
3+ 12
31
124
Answer: i honestly dont know this seems very complicated
Step-by-step explanation:
Answer:
3x^3+12x
Step-by-step explanation:
3. Write an equation of a line that is perpendicular to the line x – 2y = 8.
Answer:
y=0.5x+40
Step-by-step explanation:
Copy the equation.
x-2y=8
Subtract x from both sides.
-2y=-x-8
Divide both sides by -2.
y=0.5x+4
Now we know the slope is 0.5.
Any line with a slope of 0.5 will be perpendiculr to the original line.
One that you can use is y=0.5x+40.
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 138 lb and a standard deviation of 34.9 lb.
a. If a pilot is randomly selected, find the probability that his weight is between 150 lb and 201 lb.
b. If 39 different pilots are randomly selected, find the probability that their mean weight is between 150 lb and 201 lb.
c. When redesigning the ejection seat which probability is more relevant?
Answer:
The answer is below
Step-by-step explanation:
Given that:
mean (μ) = 138 lb, standard deviation (σ) = 34.9 lb
z score is used in statistic to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
a) For probability that his weight is between 150 lb and 201 lb, we need to calculate the z score for 150 lb and for 201 lb.
For 150 lb:
[tex]z=\frac{x-\mu}{\sigma}=\frac{150-138}{34.9}=0.34[/tex]
For 201 lb:
[tex]z=\frac{x-\mu}{\sigma}=\frac{201-138}{34.9}=1.81[/tex]
From normal distribution table, probability that his weight is between 150 lb and 201 lb = P(150 < x < 201) = P(0.34 < z < 1.81) = P(z < 1.81) - P(z < 0.34) = 0.9649 - 0.6331 = 0.3318 = 33.18%
b) If 39 different pilots are randomly selected i.e. n = 39. For probability that his weight is between 150 lb and 201 lb, we need to calculate the z score for 150 lb and for 201 lb.
For 150 lb:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{150-138}{34.9/\sqrt{39} }=2.15[/tex]
For 201 lb:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{201-138}{34.9/\sqrt{39} }=11.3[/tex]
From normal distribution table, probability that his weight is between 150 lb and 201 lb = P(150 < x < 201) = P(2.15 < z < 11.3) = P(z < 11.3) - P(z < 2.15) = 1 - 0.9842 = 0.0158 = 1.58%
c) The probability from part C is more important
The 3rd degree Taylor polynomial for cos(x) centered at a = π 2 is given by, cos(x) = − (x − π/2) + 1/6 (x − π/2)3 + R3(x). Using this, estimate cos(86°) correct to five decimal places.
Answer:
The cosine of 86º is approximately 0.06976.
Step-by-step explanation:
The third degree Taylor polynomial for the cosine function centered at [tex]a = \frac{\pi}{2}[/tex] is:
[tex]\cos x \approx -\left(x-\frac{\pi}{2} \right)+\frac{1}{6}\cdot \left(x-\frac{\pi}{2} \right)^{3}[/tex]
The value of 86º in radians is:
[tex]86^{\circ} = \frac{86^{\circ}}{180^{\circ}}\times \pi[/tex]
[tex]86^{\circ} = \frac{43}{90}\pi\,rad[/tex]
Then, the cosine of 86º is:
[tex]\cos 86^{\circ} \approx -\left(\frac{43}{90}\pi-\frac{\pi}{2}\right)+\frac{1}{6}\cdot \left(\frac{43}{90}\pi-\frac{\pi}{2}\right)^{3}[/tex]
[tex]\cos 86^{\circ} \approx 0.06976[/tex]
The cosine of 86º is approximately 0.06976.
if one tenth of a number is added to 2. the result is half of that number. what is the number?
Answer:
5
Step-by-step explanation:
According to the given question, the calculation of number is shown below:-
Let the number be x.
[tex]\frac{1}{10}[/tex] of x will be added to the number of 2, so that the result is half of x.
[tex]2 + \frac{1}{10} x = \frac{1}{2} x[/tex]
Now we will solve the above equation
[tex]2=\frac{1}{2} x-\frac{1}{10} x\\\\2=\frac{2x}{5}\\\\10=2x\\\\\frac{10}{2} =x\\\\[/tex]
x = 5
Therefore the correct answer is 5
Hence, the number based on the given information provided in the question is 5
The drama club is selling T-shirts and caps to raise money for a spring trip. The caps sell for $5.00 each, and the T-shirts sell for $10.00 each. The drama club needs to raise at least $500.00 for the trip. The inequality that represents this situation is graphed, with x representing the number of caps sold and y representing the number of T-shirts sold. Which solution is valid within the context of the situation?
Answer:
The correct answer to this question is C: (72,24).
Step-by-step explanation:
We are given that:
The cost of 1 cap is $5 each
The cost of 1 t-shirt is $10 each
Let x be the number of caps sold
Let y be the number of t-shirt sold
In the context we are given that the drama club needs to raise at least $500 to go on the trip.
So based on this information we can create a inequality as:
the number of caps sold x (times) the cost of a single cap + the number of shirts x (times) the cost of a single t-shirt ≥ (greater than or equal to) 500
Inequality: 5x+10y ≥ 500 ( We used a greater than or equal to symbol because it said that the drama club need at least $500 for the trip.
Next we need to figure out how many caps and t-shirt were sold.
- We can already take out two of the options which are the two answer with negatives in them because we know that when you multiply a positive number with a negative number we get a negative number and we don't want that. (So Option A and Option D are out.)
Now all we do is plug x and y into our inequality equation ( 5x+10y ≥ 500 )
B) x=65 caps, y= 17.5 t-shirts ----> 5(65)+10(17.5) =500 which you get $500
YOU MAY THINK THIS IS THE ANSWER BUT! if you look closely at variable y it said they sold 17.5 t-shirt, but here there thing how do you sell 17 shirts and a half of shirt? Which means this option is also wrong!
C) x =72 caps, y =24 t-shirts ------> 5(72)+ 10(24)= $600 which is more than the original amount they were going for because it said at least $500.
So the correct option to this question is C, they sold 72 caps and 24 t-shirts and earned $600 dollars.
Answer: C
Step-by-step explanation: Each coordinate point is located within the solution set, as shown on the graph.
First, take out any solution that includes a negative number, since there cannot be a negative number of bags. So, (-2,10) and (9,-3) are not solutions.
Next, take out any solution that does not have all whole numbers because the bags are whole objects. So, (4.5,9) is not a solution.
So, (8,5) is a valid solution in the context of the situation.
Find the volume of each cone.
Answer: 6 cm, V=48π or V=150.8 cm³
It appears the question is asking for the radius, but below I have shown how to find the volume.
Step-by-step explanation:
The radius is half of the diameter. The diameter of the cone of 12 cm. Half of 12 is 6. Therefore, the radius is 6 cm.
The formula to find the volume of a cone is [tex]V=\pi r^2\frac{h}{3}[/tex]. Now that we have the radius from above, we can use that to plug into the equation along with the given height.
[tex]V=\pi (6^2)\frac{4}{3}[/tex] [expand the exponent]
[tex]V=36\pi \frac{4}{3}[/tex] [combine like terms]
[tex]V=48\pi[/tex] or [tex]V=150.8 cm^3[/tex]
Solve the following for x. 3(x-2)-6x=4(x-5)
Answer:
x=2
Step-by-step explanation:
3(x-2)-6x=4(x-5)
Distribute
3x -6 -6x = 4x -20
Combine like terms
-3x-6 = 4x-20
Add 3x to each side
-3x-6+3x = 4x-20+3x
-6 = 7x-20
Add 20 to each side
-6+20 = 7x-20+20
14 = 7x
Divide by 7
14/7 =7x/7
2=x
Answer:
x = 2Step-by-step explanation:
[tex]3(x - 2) - 6x = 4(x - 5)[/tex]
Distribute 3 through the parentheses
[tex]3x - 6 - 6x = 4(x - 5)[/tex]
Distribute 4 through the parentheses
[tex]3x - 6 - 6x = 4x - 20[/tex]
Collect like terms
[tex] - 3x - 6 = 4x - 20[/tex]
Move variable to L.H.S and change it's sign
[tex] - 3x - 4x - 6 = - 20[/tex]
Move constant to RHS and change it's sign
[tex] - 3x - 4x = - 20 + 6[/tex]
Collect like terms
[tex] - 7x = - 20 + 6[/tex]
Calculate
[tex] - 7x = - 14[/tex]
Divide both sides of the equation by -7
[tex] \frac{ - 7x}{ - 7} = \frac{ - 14}{ - 7} [/tex]
Calculate
[tex]x = 2[/tex]
Hope this helps..
Best regards!!
Using traditional methods, it takes 9.5 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 15 students and observed that they had a mean of 10.0 hours with a standard deviation of 1.6. A level of significance of 0.1 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.
Answer:
Step-by-step explanation:
Null hypothesis: u = 9.5hrs
Alternative: u =/ 9.5hrs
Using the t test
t = x-u/sd/√n
Where x is 10hrs, u is 9.5, sd is 1.6 and n is 15
t = 10-9.5 / (1.6/√15)
t = 0.5 / (0.4131)
t = 1.21
In order to make a conclusion, we have to find the p value at a significance level lot 0.1. The p value is 0.2263 which is greater than 0.1. This, we will fail to reject the null hypothesis and conclude that there is not enough statistical evidence to prove that the technique performs differently than the traditional method.
G(x) = 5x + 3
Find g(b2)
Answer:
g(2) =10x+6
Step-by-step explanation:
g(x) =5x+3
g(2)=5x+3
g(2)=10x+6
have a great day
In a circle with a radius of 8ft an arc is intercepted by a central angle of 135 degrees. What is the length of the arc?
A: 6.28 ft
B: 9.42 ft
C: 18.84 ft
D: 28.26 ft
Greetings from Brasil...
We know that the entire length of a circle its:
C = 2πR
C = 2π8
C= 16π circumference length
now rule of 3:
length º
16π --------- 360
X --------- 135
360X = 135 · 16π
X = 2160π/360
X = 6π or 18,84Calculate the length of the unknown side of this right angled triangle
Answer:
12.04
Step-by-step explanation:
Well to solve for the unknown side "c" we need to use the Pythagorean Theorem formula,
[tex]a^2 + b^2 = c^2[/tex]
We already have a and b which are 8 and 9 so we plug them in.
[tex](8)^2 + (9)^2 = c^2[/tex]
64 + 81 = c^2
145 = c^2
c = 12.04 rounded to the nearest hundredth.
Thus,
the unknown side is about 12.04.
Hope this helps :)
Which of the following is equivalent to 18 minus StartRoot negative 25 EndRoot?
Answer: 12-i
12-(√-1)
Step-by-step explanation:
[tex]18-\sqrt{-25}[/tex] Original Question
[tex]18-(\sqrt{25} * \sqrt{-1} )[/tex] Split
[tex]18-5*(\sqrt{-1} )[/tex] Solve for square root
[tex]12-\sqrt{-1}[/tex] Subtract
You can substitute [tex]\sqrt{-1}[/tex] for i
[tex]12-i[/tex] Substitute
Answer:
18-5i
Step-by-step explanation:
In the given diagram, find the values of x, y, and z.
a. x = 36°, y = 36°, z = 34°
b. x = 44º, y = 44°, z = 44°
c. x = 34º, y = 34°, z = 34°
d. x = 36°, y = 34°, z = 34°
Answer:
a. x = 36°, y = 36°, z = 34°
Step-by-step explanation:
X = 36° because x and 144° are supplementary angles and the sum of supplementary angles = 180°
The sum of interior angles in a triangle is equal to 180° since one of the angle is given as 110° the sum of z and y must be equal to 70° the option that fits these qualities is a. x = 36°, y = 36°, z = 34°
Prove that tan (pi/4 + A) tan (3pi/4 +A) = -1
Answer:
Step-by-step explanation:
tan(pi\4+A)tan(3pi\4+A) =-1
using the tangent sum of angle formula
Please answer this correctly without making mistakes
Shortest is Vindale to Wildgrove to Clarksville
18.9 + 13.2 = 32.1 km.
A college financial advisor wants to estimate the mean cost of textbooks per quarter for students at the college. For the estimate to be useful, it should have a margin of error of 20 dollars or less. The standard deviation of prices is estimated to be around 100 dollars. How large of a sample size needs to be used to be 95% confident, with the given margin of error?
Answer:
minimum sample size = 97
Step-by-step explanation:
Margin of error = 20
standard deviation = 100
sample size = n
standard error = 100/sqrt(n)
confidence level, alpha = 95%
Using the standard rule for 95% confidence
standard error <= sample mean [tex]\pm[/tex] 1.96 standard error, or
20 <= 1.96*100 / sqrt(n)
n >= (1.96*100/20)^2 = 9.8^2 = 96.04
=>
n >= 97
if sin theta = 2/3 which is possible
Answer:
C. cos theta = √5/3 and tan theta = 2/√5D. sec theta = 3/√5 and tan theta = 2/√5Step-by-step explanation:
According to SOH in SOH, CAH TOA;
SOH means sin theta = opposite/hypotenuse = 2/3
This shows that opposite = 2 and hypotenuse = 3. Before we can determine which of the expression is possible, we need to find the third side of the rigt angled triangle which is the adjacent.
According to Pythagoras theorem; hyp² = opp²+adj²
adj² = hyp² - opp²
adj² = 3² - 2²
adj² = 9 - 4
adj² = 5
adj = √5
Hence the adjacent side is √5.
From the trigonometry identity above;
cos theta = adj/hyp = √5/3 and tan theta = opp/adj = 2/√5
Since sec theta = 1/cos theta then sec theta = 1/(adj/hyp)
sec theta = hyp/adj = 3/√5
From the above calculation, the following are possible:
cos theta = √5/3, tan theta = 2/√5 and sec theta = 3/√5
The correct options are C and D
WILL MAKE BRAINLIST. - - - If a golden rectangle has a width of 9 cm, what is its length?
Step-by-step explanation:
a = 14.56231 cm
b(width) = 9 cm
a+b = 23.56231 cm
A(area) = 343.1215 cm
Sorry if this doesnt help
Answer:
length = [9/2 + (9/2)sqrt(5)] cm
length = 14.56 cm
Step-by-step explanation:
In a golden rectangle, the width is a and the length is a + b.
The proportion of the lengths of the sides is:
(a + b)/a = a/b
Here, the width is 9 cm, so we have a = 9 cm.
(9 + b)/9 = 9/b
(9 + b)b = 81
b^2 + 9b - 81 = 0
b = (-9 +/- sqrt(9^2 - 4(1)(-81))/(2*1)
b = (-9 +/- sqrt(81 + 324)/2
b = (-9 +/- sqrt(405)/2
b = -9/2 +/- 9sqrt(5)/2
Length = a + b = 9 - 9/2 +/- 9sqrt(5)/2
Length = a + b = 9/2 +/- 9sqrt(5)/2
Since the length of a side of a rectangle cannot be negative, we discard the negative answer.
length = [9/2 + (9/2)sqrt(5)] cm
length = 14.56 cm
What is the measure of <A in the triangle below?
Answer:
62
Step-by-step explanation:
180-116 makes us find out that angle C is 64, thus to find out the inner angles you gotta do 64+ (2x+4)+(3x-13)=180
You follow this operation, find out x and perform 3(25)-13, which ends up giving you 62
Answer:
62°
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is not sharing a common side
2x + 4 + 3x - 13 = 116° add like terms
5x - 9 = 116°
5x = 125° divide both sides by 5
x = 25 and angle A is 3x - 13 so 3×25 - 13 = 62°
In an ANOVA the F-calculated for the treatment 4.76 with 3 degrees of freedom in the numerator and 6 degrees of freedom in the error term. What is the approximate p-value
Answer:
0.0499
Step-by-step explanation:
The p-value can be calculated using technology. The p-value is computed by using F distribution right tailed excel function. The excel function "F.DIST.RT(4.76,3,6)" gives desired p-value which is 0.0499.
The p-value shows that the for 5% level of significance the null hypothesis can be rejected.
Hermina cut a 10'' by 15'' piece of cardboard down the diagonal. A rectangle is 10 inches wide and 15 inches long. A diagonal cut is shown with a line labeled c. The cut divides the rectangle in half and creates two right triangles. The hypotenuse of each right triangle is the line labeled c. What is the length c of the cut, in inches?
Answer:
18.03 inches
Step-by-step explanation:
The cardboard is cut as shown below.
The line c cuts the rectangle into 2 right angled triangles.
To find the diagonal (hypotenuse), we have to apply Pythagoras Rule:
[tex]hyp^2 = opp^2 + adj^2\\\\=> c^2 = 10^2 + 15^2\\\\c^2 = 100 + 225 = 325\\\\[/tex]
=> c = 18.03" = 18.03 inches
The length of c, the diagonal, is 18.03 inches.
is the midsegment of ABC. If is 30 centimeters long, how long is ?
A.
25 centimeters
B.
20 centimeters
C.
15 centimeters
D.
10 centimeters
Answer:
C. 15 centimeters
Step-by-step explanation:
The Triangle Midsegment Theorem
segment LM = 1/2 of AC
LM = 1/2 * 30
LM = 15 cm
Two trains leave New York at the same time heading in opposite directions. Train A travels at 4/5 the speed of train one. After seven hours they are 693 miles apart. What was the speed of train A? Can you pls help me fast
=============================================
Work Shown:
x = speed of train A
y = speed of train B
"train A travels 4/5 the speed of train B" (I'm assuming "train one" is supposed to read "train B"). So this means x = (4/5)y
distance = rate*time
d = x*7
d = (4/5)y*7 = (28/5)y represents the distance train A travels
d = y*7 = 7y represents the distance train B travels
summing those distances will give us 693
(28/5)y + 7y = 693
5*( (28/5)y + 7y ) = 5*693
28y + 35y = 3465
63y = 3465
y = 3465/63
y = 55
Train B's speed is 55 mph
4/5 of that is (4/5)y = (4/5)*55 = 4*11 = 44 mph
Train A's speed is 44 mph
Adult men have heights that a normally distributed with a mean of 69.5 inches and a standard deviation of 2.4 inches. Adult women have heights that a normally distributed with a mean of 63.8 inches and a standard deviation of 2.6 inches. Between a man with a height of 74 inches and a women with a height of 70 inches, who is more unusually tall within his or her respective sex ?
Answer:
Step-by-step explanation:
From the information given:
For Adult Men
Mean [tex]\mu[/tex] = 69.5
Standard deviation [tex]\sigma[/tex] = 2.4
observed value X = 74
For Adult Women
Mean [tex]\mu[/tex] = 63.8
Standard deviation [tex]\sigma[/tex] = 2.6
observed value X = 70
Therefore ; the values for their z scores can be obtained in order to determine who is more unusually tall within his or her respective sex
For Adult Men :
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]z = \dfrac{74- 69.5}{2.4}[/tex]
[tex]z = \dfrac{4.5}{2.4}[/tex]
z = 1.875
For Adult Women :
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]z = \dfrac{70- 63.8}{2.6}[/tex]
[tex]z = \dfrac{6.2}{2.6}[/tex]
z = 2.3846
Thus; we can conclude that , the women is more unusually tall within his or her respective sex
A local theatre sells out for their show. They sell all 500 tickets for a total purse of $8,040.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults. If the band sold three times as many adult tickets as children's tickets, how many of each type were sold?
Answer:
number of children ticket sold = 70
number of adult ticket sold = 70 × 3 = 210
number of student ticket sold = 500 - 4(70) = 500 - 280 = 220
The number of Adult's ticket sold = 270, Children's ticket sold = 90 and Student's ticket sold = 140.
What is an expression? What is a expression? What is a mathematical equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have a local theatre that sells out for their show. They sell all 500 tickets for a total purse of $8,040.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults.
Adult's ticket = [y]
Children's ticket = [x]
Student's ticket = [z]
and
y = 3x
Now -
x + y + z = 500
x + 3x + z = 500
4x + z = 500 ....[1]
and
12x + 18y + 15z = 8040
12x + 18(3x) + 15z = 8040
12x + 54x + 15z = 8040
66x + 15z = 8040 ....[2]
On solving [1] and [2], we get -
x = 90 and z = 140
and
y = 3x = 3 x 90 = 270
y = 270
Therefore, the number of Adult's ticket sold = 270, Children's ticket sold = 90 and Student's ticket sold = 140.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
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