at a basketball game, a vender sold a combined total of 166 sodas and hot dogs. The number of hot dogs sold was 54 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold. ​

Answers

Answer 1

The best way to solve these sorts of problems that involve two factors of unknown quantities but with certain properties is to use equations:

Let's set some variables

h: # of hot dogs solds: # of sodas sold

Now based on the information given by the question, let's set up some equations:

 vender sold a combined total of 166 sodas and hot dog

              ⇒ [tex]s + h = 166[/tex]

number of hot dogs sold was 54 less than the number of sodas sold

             ⇒ h = s - 54

Now lets put the equation together

  s + h = 166 -- equation 1

  h = s - 54   -- equation 2

Solve:

  Plug the value of h from equation 2 into equation 1

      s + (s - 54) = 166

        2s - 54 = 166

           2s = 220

             s = 110 -- equation 3

   Plug the value of s from equation 3 into equation 2

      h = 110 - 54 = 56

            h = 56

Therefore:

number of sodas sold: 110number of hot dogs sold: 56

Hope that helps!


Related Questions

What is the smallest angle of a right triangle with sides 9, 40, and 41? Round your answer to the nearest degree, and enter the number only.​

Answers

Answer: 13°

Explanation: x = tan^-1 ( 9/40) ≈ 13°

Lela bought 3.3 pounds of nuts they cost $1.79 a pound. How much money did she spend

Answers

Answer:

5.907

Step-by-step explanation:

I believe if you multiply 3 times 1.79 you get 5.37 then if you multiply 0.3 times 1.79 you get 0.537. If you combine the 2 you get 5.907. I think this is correct not sure though D:

7(5/14a-5/21)-1/12(3a+6)

Answers

[tex]\sf \dfrac{9a}{4}-\dfrac{13}{6}[/tex]      or     [tex]\sf \dfrac{54a-52}{24}[/tex]

======================================

[tex]\sf \rightarrow 7\left(\dfrac{5}{14}a-\dfrac{5}{21}\right)-\dfrac{1}{12}\left(3a+6\right)[/tex]

use distributive method

[tex]\sf \rightarrow \dfrac{5a}{2}-\dfrac{5}{3}-\dfrac{a}{4}-\dfrac{1}{2}[/tex]

group terms

[tex]\rightarrow \sf \rigtharrow \dfrac{5a}{2}-\dfrac{a}{4}-\dfrac{5}{3}-\dfrac{1}{2}[/tex]

make the denominators same

[tex]\rightarrow \sf \rigtharrow \dfrac{2(5a)}{4}-\dfrac{a}{4}-\dfrac{2(5)}{6}-\dfrac{3(1)}{6}[/tex]

simplify

[tex]\rightarrow \sf \rigtharrow \dfrac{10a-a}{4}-\dfrac{10+3}{6}[/tex]

answer in separate constants

[tex]\rightarrow \sf \dfrac{9a}{4}-\dfrac{13}{6}[/tex]

make the denominators same

[tex]\rightarrow \sf \dfrac{6(9a)}{24}-\dfrac{4(13)}{24}[/tex]

simplify

[tex]\rightarrow \sf \dfrac{54a}{24}-\dfrac{52}{24}[/tex]

join both fractions

[tex]\rightarrow \sf \dfrac{54a-52}{24}[/tex]

Answer:

 [tex]\boxed{\dfrac{9a}{4} - \dfrac{7}{6}}[/tex]

Step-by-step explanation:

[tex]7(\dfrac{5a}{14} - \dfrac{5}{21} ) - \dfrac{(3a + 6)}{12}[/tex]

Step-1: Simplify the distributive property

⇒ [tex]\dfrac{35a}{14} - \dfrac{35}{21} - \dfrac{(3a + 6)}{12}[/tex]

Step-2: Make common denominators

⇒ [tex]\dfrac{35a \times 3}{14 \times 3} - \dfrac{35 \times 2}{21 \times 2} - \dfrac{7 \times (3a + 6)}{12 \times 7}[/tex]

⇒ [tex]\dfrac{210a}{84} - \dfrac{140}{84} - \dfrac{7 \times (3a + 6)}{84}[/tex]

Step-3: Simplify the distributive property

⇒ [tex]\dfrac{210a}{84} - \dfrac{140}{84} - \dfrac{21a + 42}{84}[/tex]

Step-4: Rewrite (21a + 42)/84 in a different way

⇒ [tex]\dfrac{210a}{84} - \dfrac{140}{84} - \dfrac{21a}{84} + \dfrac{42}{84}[/tex]

Step-5: Add/Subtract if necessary

⇒ [tex]{\dfrac{189a}{84} - \dfrac{98}{84}}[/tex]

Step-6: Simplify the fractions

⇒ [tex]{\dfrac{189a}{84} - \dfrac{98}{84}} = {\dfrac{9a}{4} - \dfrac{49}{42}} = \boxed{\dfrac{9a}{4} - \dfrac{7}{6}}[/tex]

please help me please pleasr please

Answers

Answer:

which one's anwer you want

2. length= 65 ft width=24 m area=135 in2

I don’t know what is the least common factor of 18 and 12.

Answers

Answer:

the common factors for both are 1,2,3,6

is this correct?

A.yes

B. No

C. Maybe

D. I DUNNO???!!!

Answers

Answer:

its yes

Step-by-step explanation:

because it's x 2  I hope this helps      

 

am I right? please only answer if you are positive that you’re correct. thank you!

Answers

Answer:

yes you are correct :)))

Give the dimensions of 2 solids with equal surface area and different volume

Answers

Two solids with the same surface and different volumes are a cube of side length of 1 unit, and a sphere of radius of 0.69 units.

How to find the two solids?

First, let's define a cube of a side length of 1 unit. The surface of this cube is equal to 6 times the area of one of the faces, or:

S  = 6*(1 unit square) = 6 units square.

And the volume is equal to the side length cubed, so we have:

V = (1 unit)^3 = 1 unit cubed.

Now, let's find a sphere with the same surface than our cube. For a sphere of radius R, the surface is:

S = 4*3.14*R^2

Then we must have:

4*3.14*R^2 = 6 units square

R = √(6/(4*3.14)) units = 0.69 units.

And the volume of this sphere is:

V = (4/3)*3.14*R^3 = (4/3)*3.14*(0.69 units)^3 = 1.38 cubic units.

So the sphere has the same surface and more volume.

If you want to learn more about solids, you can read:

https://brainly.com/question/10171109

Determine the perimeter of the figure below:
6 cm
5 1/2


helpppp

Answers

Answer:

•SEE BELOW•

WHAT IS PERIMETER?

>> PERIMETER MEANS THE SUM OF ALL SIDES OF FIGURE

NOW,LET'S SEE YOUR GIVEN QUESTION.

THE FIGURES 2 SIDES DATA IS GIVEN

6CM

5.5CM

THEREFORE : 6 + 5.5

: 11.5 CM

THE PERIMETER OF FIGURE IS 11.5 CM


The first term of an A.P is 3 and the fifth term is 9.Find the number of terms in the progression if the sum of the progression is 81.​

Answers

Answer:

its A becauss i tryed b and th en i tried A so its a

I need help please give explanation and thank you

Answers

Area of semi circle is 0.5 (pie*radius^2)

Area of triangle = 0.5(width*height )

50% of the population are within one standard deviation.
O True
O False ???

Answers

Answer: False

Step-by-step explanation:

68%

Key Takeaways. The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.

Let a represent a non zero rational number and let b represent an irrational number. Which expression could represent a rational number?

Answers

The operation between a rational and a irrational number that results in a rational number is a multiplication, hence the expression ab could represent a rational number.

What are rational and irrational numbers?

If a number can be represented by a fraction, it is rational, otherwise, it is irrational.

The addition/subtraction of a rational and an irrational numbers is irrational, while the multiplication is rational, hence the expression ab could represent a rational number.

More can be learned about rational numbers at https://brainly.com/question/10814303

A vet is preparing a diet for a group of dogs. Each serving should be no larger than 8
ounces and must contain at least 29 units of Nutrient I and at least 20 units of Nutrient II.
The diet will be prepared from a combination of 2 brands, brand A and brand B. Each ounce
of brand A contains 3 units of Nutrient I and 4 units of Nutrient II. Each ounce of brand B
contains 5 units of Nutrient I and 2 units of Nutrient II. Brand A costs 3 cents/ounce and B
costs 4 cents/ounce. Determine how many ounces of each brand of dog food should be used
per serving in order to meet the given requirements at a minimum cost.

Answers

5 maybe but prob A or B

Find the 18th term in the arithmetic sequence.
2, 8, 14, 20, 26, ...
87
110
104
102

Answers

I’m pretty sure it is 2

Answer:

104

Step-by-step explanation:

1st term + or - common difference (term -1)

common difference is +6

2 + 6 (18-1)

2 + 6 (17)

2 + 102

104

Tori made a scale drawing of an Italian
restaurant. The restaurant's kitchen is 2
millimeters long in the drawing. The actual
kitchen is 16 meters long. What scale did Tori
use for the drawing?
1 millimeter :
meters

Answers

Step-by-step explanation:

2mm : 16m

so to get 1mm you need to divide 16 by 2

16/2 is 8 therefore

1mm : 8m

1 millimeter represents 8 meters in real life

hope that helps :)

how do i solve this?

Answers

Answer:

33

Step-by-step explanation:

For 4 triangles area 4*(1/2)*4*3=24

base square area 3*3=9

all together 24+9= 33  

can someone please help me with this question???? its an exam study guide and i dont understand it

Josef owns four par value $1,000 bonds from Dowc Beverage Co. Each bond has a market value of 104.561 and gives 9.2% interest. Josef also owns 170 shares of stock in Dowc Beverage Co. Stock in Dowc Beverage Co. has a share price of 26.25 and pays a dividend of $2.38. If the broker Josef employed to purchase these stocks and bonds charges a commission of $72 for each ten shares of stock bought or sold and a commission of 4% of the market value of each bond bought or sold, which aspect of Josef’s investment in Dowc Beverage Co. has a greater percent yield, and how much greater is it?
a.
The stocks have a yield 2.15 percentage points higher than that of the bonds.
b.
The stocks have a yield 0.27 percentage points higher than that of the bonds.
c.
The bonds have a yield 1.35 percentage points higher than that of the stocks.
d.
The bonds have a yield 2.08 percentage points higher than that of the stocks.

Answers

Answer:

If the broker Josef employed to purchase these stocks and bonds charges a commission of $72 for each ten shares of stock bought or sold and a commission of 4% of the market value of each bond bought or sold, then the bonds have a yield 1.35 percentage points higher than that of the stocks.

Step-by-step explanation:

Help picture below problem 11

Answers

Answer:

Missing Angle = 26⁰ ( corresponding angles )

PLEASE HELP PLEASE PLEASE HELP

Answers

Answer:

I believe it is Dissolve.

please help and please leave a legit answer

Answers

Answer:

y= -12/x + 3

Step-by-step explanation:

Here's my answer

Why 10^33/2=5*10^32? Explain, pls. :(

Answers

Answer:

see below

Step-by-step explanation:

10^33/2

Rewriting the numerator as 10 * 10 ^ 32

10 * 10 ^32

--------------------

2

10/2 = 5

5 * 10 ^32

Therefore

10^33/2=5*10^32

Factor the equation 4x^2-20x+25

Answers

Answer:

[tex](2x - 5)^2[/tex]

Step-by-step explanation:

[tex]y = 4x^2 -20x + 25\\\rightarrow (2x - 5)(2x - 5)\\\rightarrow (2x - 5)^2\\\\\text{checking...}\\(2x - 5)^2 = (2x - 5)(2x - 5) = 4x^2 - 10x - 10x + 25 = 4x^2 - 20x + 25[/tex]

Solve for x. Round to the tenths place. Can somebody help

Answers

Answer:

12.12

Step-by-step explanation:

7^2+x^2=14^2, as by the Pythagorean theorem.

49+x^2=196,

x^2=147,

square root of 147;

it's close to 144,

thus, 12.12

A rectangular playground measures 5/8 mile long and 1/4 mile wide. What is the area, in square miles, of the playground?

Answers

Answer:

5/32 square miles or 0.15625 square miles

Step-by-step explanation:

1/4 miles × 5/8 miles

=5/32 square miles or 0.15625 square miles

Find the domain and range of the function graphed below.
Domain:
Range:

Answers

The domain of the function is [-2, 2) while the range is [4, 2) (along the y -axis).

How to find the domain and range of a function

The domain of a function is the input value for which the function exists while the range is the output value for which the function exists.

For the graph, the domain lie across the x-axis. The domain of the function is [-2, 2) while the range is [4, 2) (along the y -axis).

Note that point where the circles are shaded shows a closed interval

Learn more on domain and range here: https://brainly.com/question/1942755

BRAINLIEST GIVEN)The figure is the net for a rectangular prism.
What is the surface area of the rectangular prism represented by the net?



Enter your answer in the box.

Answers

Answer:

238

Step-by-step explanation:

You have to find the area for each box and then you add all of them together

Answer:

238 mm²

Surface area of rectangular prsim = 2(lw + lh + wh)

Here,

length = 11 mm

width = 4 mm

height = 5 mm

area:

2*(4*11+5*11+5*4)238 mm²

Select the correct answer. The total cost of a flower bouquet depends on the types of flowers in the arrangement. A bouquet containing 6 roses, 3 lilies, and 2 carnations costs $26.75. A bouquet containing 3 roses, 4 lilies, and 5 carnations costs $25.50. A bouquet containing 1 of each flower costs $6.75. Which system of equations represents this situation, where rrepresents the number of roses, /represents the number of lilies, and c represents the number of carnations?​

Answers

Answer: Roses 2.70 Lillies 2.45 Carnations 1.60

Step-by-step explanation:

I dont know if its wrong its mostly correct but hope it helps

Two gears are connected and rotating at the same time. The smaller gear completes 2 1/2 rotations every time the larger gear completes 1/4 of a rotation.


How many rotations does the smaller gear complete when the larger gear completes 1 rotation?


A.1/10

B. 5/8

C. 5

D. 10

Answers

The small does 2 1/2 for 1/4 of the large. Multiply by 4 to get a full rotation of the large one:


2 1/2 x 4 = 10


answer: D. 10

A pool measuring 10 meters by 26 meters is surrounded by a path of uniform​ width, as shown in the figure. If the area of the pool and the path combined is 1380 square​ meters, what is the width of the​ path?

Answers

Answer:

112m

Step-by-step explanation:

A = lw

A = 10(26)

A = 260

1380 - 260 = 1120

1120 = 10(w)

1120 / 10 = 112

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