1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vsevolod [243]
3 years ago
13

A youth group is selling snacks to raise money to attend their convention. Amy sold 2 pounds of candy, 3 boxes of cookies and 1

can of popcorn for a total sale of $65. Brian sold 4 pounds of candy, 6 boxes of cookies and 3 cans of popcorn for a total sale of $140. Paulina sold 8 pounds of candy, 8 boxes of cookies and 5 cans of popcorn for a total sales of $250. What is the cost of each item
Mathematics
1 answer:
asambeis [7]3 years ago
8 0

Answer:

The cost of a can of popcorn is $10.

The cost of a box of cookies is $5.

The cost of a can of popcorn is $20

Step-by-step explanation:

First you must propose a system of equations, a set of two or more equations with several unknowns in which you want to find the value of each unknown so that all the equations of the system are fulfilled.

Defining the variables:

  • x: cost of one pound of candy
  • y: cost of a box of cookies
  • z: cost of a can of popcorn

Amy sold 2 pounds of candy, 3 boxes of cookies and 1 can of popcorn for a total sale of $65. Then:

2*x + 3*y + 1*z=65 Equation 1

Brian sold 4 pounds of candy, 6 boxes of cookies and 3 cans of popcorn for a total sale of $140. So:

4*x + 6*y + 3*z=140 Equation 2

Paulina sold 8 pounds of candy, 8 boxes of cookies and 5 cans of popcorn for a total sales of $250. Then:

8*x + 8*y + 5*z=250 Equation 3

Then the system of equations is formed by these three equations.

A method to solve a system of equations is by means of the substitution method, which consists of isolating one of the two unknowns in an equation to substitute it in the other equation.

Isolating z from Equation 1:

z=65-2*x-3*y Equation 4

Replacing in Equation 2:

4*x + 6*y + 3*(65 -2*x-3*y)=140

4*x + 6*y + 195 - 6*x  - 9*y= 140

-2*x - 3*y=140-195

-2*x - 3*y=-55

2*x + 3*y= 55

and isolating x:

x=\frac{55-3*y}{2} Equation 5

Replacing in Equation 4:

z=65-2*\frac{55-3*y}{2} -3*y

z=65 - (55-3*y) - 3*y

z= 65 -55 + 3*y - 3*y

<u><em>z= 10</em></u>

<u><em>So the cost of a can of popcorn is $10.</em></u>

Replacing equation 5 and the value of z in equation 3:

8*\frac{55-3*y}{2} + 8*y + 5*10=250

\frac{8}{2}*(55 -3*y)+ 8*y + 5*10=250

4*(55 -3*y)+ 8*y + 5*10=250

4*55 - 4*3*y + 8*y + 50=250

220 - 12*y + 8*y + 50=250

-12*y + 8*y= 250 -220 - 50

-4*y= -20

y=\frac{-20}{-4}

<u><em>y= 5</em></u>

<u><em>So the cost of a box of cookies is $5.</em></u>

Finally replacing the value of y in Equation 5 you get the value of x:

x=\frac{55-3*5}{2}

x=\frac{55-15}{2}

x=\frac{40}{2}

<u><em>x=20</em></u>

Finally,<u><em> the cost of a can of popcorn is $20</em></u>

You might be interested in
Use formula I=prt to solve:
kvv77 [185]

Answer: $175.50

Step-by-step explanation: Since you are given the formula, your next step is to put your information into it.

I = PRT

I = 450 x .13 x 3

Now to solve for it:

I = $175.50

6 0
3 years ago
To factor 9x^2-16 you can first rewrite the expression as:
natka813 [3]
I hope this helps you

4 0
3 years ago
Please help, am i right
earnstyle [38]

Answer: yea you are

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
seven pounds of potatoes were used to make a potato soup. the cook served all of the soup in sixteen equal servings. how many po
marshall27 [118]

Answer:

0.4375

Step-by-step explanation:

7/16=0.4375

If you have any additional questions let me know. :)

8 0
3 years ago
Norman is shipping 2 boxes. the first box weighs 4180 grams and the second box weighs 820 grams. if shipping costs $6.43 per kil
gregori [183]
Total cost is: $<span>32.15

</span>
3 0
3 years ago
Read 2 more answers
Other questions:
  • A school has 415 third graders and 338 second graders home many more third graders are there than second graders
    10·1 answer
  • Simplify <br><br> 2√10 * 3√12<br><br> Please don’t guess I beg u
    14·1 answer
  • Todd caught at least three times as many fish this year as he did last year. He caught 63 fish this year. Write an inequality th
    14·1 answer
  • 3x+2y=-4<br> y= 4x-2<br> use substitution
    13·2 answers
  • Which graph shows the image being rotated 90°?
    12·2 answers
  • Write a real life scenario that can be represented by the integer –55.
    11·1 answer
  • What is the first step when applying properties of operations to divide 73.85 by 4.1?
    8·1 answer
  • 2 = 9 + 5/2 <br> please answer this
    5·2 answers
  • E = MV^2 ÷ 2 + mgh, Make V Subject of the formula​
    13·1 answer
  • Calculate the distance between the points E= (-9,8) and M= (-4,2) in the coordinate plane. Give an exact answer (not a decimal a
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!