Jack has $37 and saves $6.50 per week. Diane has $9 and saves $8.25 per week. Define a variable, then write and solve an equation to find out how many weeks it would take for Jack and Diane to have saved the same amount of money.​

Answers

Answer 1

Answer:

Defining variable: x = per week

Equation: 37 + 6.5x = 9 + 8.25x

Answer: 16 weeks

Step-by-step explanation:

x = per week

Jack:

37 + 6.5x

Diane:

9 + 8.25x

Equation:

37 + 6.5x = 9 + 8.25x

6.5x - 8.25x = 9 - 37

-1.75x = -28

x = 16

Answer 2

The number of weeks when Jack and Diane would have the same amount of money is 16 weeks.

Equations that represents the amount of money saved

Total amount of money saved = amount the person has + (amount the person saves per week x number of weeks)

Total amount of money Jack saves = $37 + ($6.50 x w)

Total amount of money Diane saves = $9 + ($8.25 x w)

Number of weeks when they would have the same amount of money

When Jack and Diane would have the same amount of money, the equations that represent the total amount of money saved for both individuals would be equal.

$37 + $6.50w = $9 + $8.25w

combine similar terms

$37 - $9 = $8.25w - $6.50

$28 = 1.75w

Divide both sides of the equation by 1.75

w = 16 weeks.

To learn more about how to determine when two people would have equal quantities, please check: https://brainly.com/question/25711114


Related Questions

Alice has 5 quarters and 2 nickels. How many cents does Alice have

Answers

Answer:

Alice has 135 cents, or $1.35.

Step-by-step explanation:

A quarter is worth 25 cents.A nickel is worth 5 cents.Multiply 25 by 5, since there are 5 quarters. That will give you 125.Multiply 5 by 2, since there are 2 nickels. That will give you 10.Add 125 and 10. That will give you 135, which is your answer!

A stationery store wants to estimate the mean retail value of greeting cards that it has in its inventory. A random sample of 15 greeting cards indicates an average value of $3.00 and a s of $0.40. The critical value for a 99% confidence interval is

Answers

Answer:

The critical value for a 99% confidence interval is T = 2.9768

Step-by-step explanation:

We have the standard deviation of the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 15 - 1 = 14

Critical value

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.9768

The critical value for a 99% confidence interval is T = 2.9768

someone please help me answer this!!!

Answers

Answer:

15 using the Pythagorean theorem.

hope it helps, plz mark me as brainliest.

Answer:

15 units is the answer.

Step-by-step explanation:

points are (-3,-4) and (6,8)

Pythagorean theorem can be written as,

[tex]d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\\\d=\sqrt{(6-(-3))^2 + (8-(-4))^2}\\\\d=\sqrt{(9)^2+(12)^2} \\\\d=\sqrt{81+144} \\\\d=\sqrt{225} \\\\d=15[/tex]

∴ d = 15 units is the distance between the points.

Please please help please

Answers

Answer: 72 feet

Step-by-step explanation:

24 yards= 72 feet

72 feet bc that equals that

2. 48 degrees 17 x
(solve for x. round to the nearest tenth)

Answers

Answer:

67

Step-by-step explanation:

you divide the 48/17 yo get 67

A large clock in a town square has a minute hand that is 10 feet long. Which value is the best estimate of
how many degrees the minute hand moves from 4:00 - 4:40?

Answers

Answer: 240 degrees

Step-by-step explanation: minute hand makes 360 degree circle in hour.

There is no influence for the length of hand in this case.

40 minutes is 2/3 hours. 2/3 ·360 degrees

convert 320% to an equivalent decimal.​

Answers

Answer:

Answer is 3.2

Step-by-step explanation: you can take any percent and divide it by 100. So in this example you would divide 320/100 and it will give you 3.2

Which is the greater decimal?

.721 or .72

Answers

Answer:

.721 is bigger because Il earned that the decimal that has a larger number as there last number is the greatest decimal.

Step-by-step explanation:

Solve the system of equations.
2.5y+ 3x = 27
5x-2.5y = 5
What equation is the result of adding the two equations?
What is the solution to the system?​

Answers

Answer:

The asnwer to the system of equation

x=4 y=6

Step-by-step explanation:

Answer:  1) 8x=32       2) (4,6)

Step-by-step explanation:

Hope this helps!

Mark me brainliest!

Pls and ty!

Cassandra works for a company that is based off her sales. If she is paid 9.5% of her total monthly sales, calculate her pay for the month if she sells $15,670 of product.

Answers

Answer:

I don't understand what you mean. but 10.43 i guess

The arch support of a bridge can be modeled by y=−0.0012x2, where x and y are measured in feet. Find the height and width of the arch.

Answers

Answer:

it will be 300 feet tall and 1000 feet wide

Step-by-step explanation:

The height and width of the arch which support of a bridge and modeled by the provided function is 1000 ft and 300 ft long respectively.

What is an exponential function?

Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.

The exponential function with dependent variable y and independent variable x can be written as,

[tex]y=ba^x+c[/tex]

Here, a,b and c are the real numbers.

The arch support of a bridge can be modeled by the following function,

[tex]y=-0.0012x^2+300[/tex]

Here, x and y are measured in feet.

The height and width of the arch has to be found out. First, find the x intercept of the function. As at the x intercept, the y equal to zero. Therefore,

[tex]0=-0.0012x^2+300\\0.0012x^2=300\\x=\sqrt{25000}\\x=500[/tex]

As, the graph is symmetric around the y-axis. Thus, the -500 can also be a solution. Now, the width of the arch can be given as,

[tex]w=500-(-500)\\w=1000\rm ft[/tex]

Now similarly at x equal to zero, the function will be,

[tex]y=300[/tex]

Hence, the height and width of the arch which support of a bridge and modeled by the provided function is 1000 ft and 300 ft long respectively.

Learn more about the exponential function here;

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Mrs.Hilt’s yard is 48 feet long and 39 feet wide . What is the area of Mrs.Hilt’s back yard?

Answers

Answer:

               1872

Step-by-step explanation

Please help me with this question if you can

Answers

Answer:

exterior angle = the sum of two remote interior angles

14x + 1 = 89 + 5x - 7

=> 9x = 81

=> x = 9

substitute x = 9 into angle H (5x - 7)

=> 5(9) - 7 = 45 - 7 = 38

What is the solution of the equation?

Answers

Answer:

+8 and -8, 2nd answer from the right.

What is 1/6 as a percent.

Answers

Answer:

16.66 %

Step-by-step explanation:

1 / 6 as a percent

= ( 1 / 6 ) x 100

= 100 / 6

= 16.66 %

1/6 = 16.6667% (percentage)

What is the square root of –16?
A. –8i
B. –4i
C. 4i
D. 8i

Answers

Answer:

C. 4i

Step-by-step explanation:

Answer:

C. 4i

Step-by-step explanation:

[tex]\sqrt{-16} = \sqrt{16} \sqrt{-1}[/tex] (because [tex]\sqrt{ab} =\sqrt{a} \sqrt{b}[/tex])

Since [tex]\sqrt{16}[/tex]=4, and [tex]\sqrt{-1}[/tex]=i, [tex]\sqrt{-16}[/tex]=4i

Help me with these problem as an area of a circle.

Answers

Area of circle = pi * r^2
pi * (3.25)^2 = 33.18307

Rounded = 33.18
Solution: area = 33.28 yd^2

Answer:

33.18

Step-by-step explanation:

Using the formula in the image below, substitute [tex]r[/tex] for [tex]3\frac{1}{4}[/tex], and simplify π to about 3.14. Then solve that. [tex]3.14((3\frac{1}{4})^{2})=33.18[/tex]

A car and a truck left Washington, DC traveling in opposite directions. The car traveled 19 miles per hour faster than the truck, and at the end of 8 hours they were 1048 miles apart. What was the average speed of each vehicle?

100 POINTS

Answers

Answer:

Step-by-step explanation:xmccc

Truck speed be x
Car travel at x+19
They travel in opposite directions so the separation is (x+x+19) * no. Of the hours
1048 = (2x+19)*8
X= ((1048/8)-19)/2
=56

Truck speed is 56 miles per hour
Car speed is 56+19=75 miles per hour

3/4+1/2= 2. 5/6+1/2= 3. 3/6+1/2= 4.1/6+4/8= 5.7/8+1/4= 6.3/8+1/2=

Answers

Answer:

1.) [tex]\frac{5}{4\\}[/tex]

2.) [tex]\frac{4}{3}[/tex]

3.) 1

4.) [tex]\frac{2}{3}[/tex]

5.) [tex]\frac{9}{8}[/tex]

6.) [tex]\frac{7}{8}[/tex]

Step-by-step explanation:

The 2 steps for all of these is to get common denominators and then add and simplify.

1.) 3/4 + 1/2 (common denominator) 3/4 + 2/4 = 5/4

2.) 5/6 + 1/2 (common denominator) 5/6 + 3/6 = 4/3

3.) 3/6 + 1/2 (common denominator) 3/6 + 3/6 = 6/6 (simplify) = 1

4.) 1/6 + 4/8 (common denominator) 8/48 + 24/48 =  32/48 (simplify) = 2/3

5.) 7/8 + 1/4 (common denominator) 7/8 + 2/8 = 9/8

6.) 3/8 + 1/2 (common denominator) 3/8 + 4/8 = 7/8

A plane is already 44 cm tall and it will grow in one centimeter every month let H be the plants height in centimeters after M months write an equation relating H to M. Then use the equation to find a plant's height at 14 months

Answers

Answer:idea I jus wanna get my answers answered sk 3728 okay??

Step-by-step explanation:!3$:$::$2$:773727/

Y=1/4 x + 2 which is the equation of a line parallel to the line with the equation

Answers

The answer is y=1/4x

Jasmine was expected to get $150 for her bonus, but she only got $100. What was the percent error?

Answers

Answer:

Jasmine expected to get $150 for her bonus, but she only got $100. What was the percent error?

-----

Amt of error:: $50

----------

% error:: 50/150 = 1/3 = 33 1/3%

Hudson is going to invest $320 and leave it in an account for 9 years. Assuming the
interest is compounded monthly, what interest rate, to the nearest tenth of a percent,
would be required in order for Hudson to end up with $540?

Answers

Answer:

5.8

Step-by-step explanation:

The interest rate, to the nearest tenth of a percent, will be 0.05828.

How do you determine the amount of compound interest?

If the principal amount is P, the interest rate is R percent per unit time, and the compound interest is left for T units of time, the interest amount gained is:

[tex]\rm CI = P\left(1 +\dfrac{R}{100}\right)^T - P[/tex]

The total is:

[tex]\rm A = CI + PA = P(1 +\dfrac{R}{ 100})T[/tex]

The amount is found as;

[tex]\rm A = P(1+\frac{r}{n})^{nt}\\\\ 540=320 (1+\frac{r}{12} )^{12\times 9}\\\\ (1+\frac{r}{12})^{108}=\frac{540}{320}\\\\ 1+\frac{r}{12}=(\frac{540}{320})^{\frac{14}{108}[/tex]

[tex]\rm 1+ \frac{r}{12}=1.00486\\\\ \frac{r}{12}=0.00486\\\\ r=12 \times 0.0486 \\\\ r=0.05828[/tex]

Hence, the interest rate, to the nearest tenth of a percent, will be 0.05828.

To learn more about compound interest, refer:

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#SPJ2

i need number 22 PLS AND THANK YOU!

Answers

Answer:

For any two given points (x1,y1) and (x2,y2), the slope = (y2-y1)/(x2-x1)

Let's take the points (15,3) and (30, 6):

slope = (y2-y1)/(x2-x1)

= (6-3)/(30-15)

=3/15

=1/5 =0.2

The slope, in general, means the rate of change of y, relative to x. In the context of this question, the slope tells us that the amount of concrete that can be poured (in yards) is a fifth of the time taken (in minutes).

An introductory psychology class has 9 freshman males, 15 freshman females, 8 sophomore males, and 12 sophomore females. A random sample of n = 2 students is selected from the class. If the first student in the sample is a male, what is the probability that the second student will also be a male?

Answers

Answer

16/43

Step-by-step explanation:

17 Male + 27 female = 44 students

now n= 2 so first student was male so one male student was taken out of the equation so 16 male left. now left male students by remaining students  so now total left students = 43

so, prob = remaining males/remaining students=16/43

From the equation y = 4 - X, which ordered pair would represent a solution?
A (3,-1)
B (9,5)
C (6,-2)
D (0,-4)

Answers

I think it’s D hope that helped
Let’s rewrite the equation in y=mx+b
y=-x+4
The slope is -x or -1x. Rise 1, run 1
The y intercept is 4
Start from 4 on the y axis and move down 1 and right 1.
The line will cross point (6,-2)
Answer C

Help me answer these

Answers

Step-by-step explanation:

y=-2X2 -2X +4

Answer: I answered it it's C

it’s C but you can use Photomath

Calculate the finance charge for a credit card that has an average daily balance of Php5,600 and a monthly interest rate of 1.35 %

Answers

Answer:The simplest way to calculate a finance charge is: balance X monthly rate

Step-by-step explanation:

i thinkk

500 X .015 = $7.50

The finance charge for a credit card that has an average daily balance of 5,600 and a monthly interest rate of 1.35 % is $75.6.

What is the finance charge?

The finance charge is the product of an average daily balance to the monthly interest rate.

finance charge = balance x monthly rate

The simplest way to calculate a finance charge = balance x monthly rate

= 5,600 x 0.0135

= $75.6

Thus, the finance charge for a credit card that has an average daily balance of 5,600 and a monthly interest rate of 1.35 % is $75.6.

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Rewrite 7^-2 using a positive exponent an evaluate the result.

Answers

positive exponent= 1/7^2
evaluate=1/49

What is the value of B?

Answers

Answer:

The value of B is 0 because going down from the middle is all negative and going up from point B is all positive so the answer is 0 degrees

Step-by-step explanation:

Answer:

in linear pair

90+a+24=180

a=180-90-24=66°

B°=90+a=90+66=156°

the value of B°=156°

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