How many bottles of each ingredient?

Question

You spend $22 buying ingredients for fruit punch. Each 32-ounce bottle of

pineapple juice, apple juice, and ginger ale costs $2.50, $2.00, and $1.50,

respectively. The recipe calls for the amount of ginger ale to equal the

combined amount of pineapple juice and apple juice. You buy a total of

12 bottles. How many bottles of each ingredient do you buy? Write a system of equations.

Answer 1

Hi Taylor

Fruit Punch made with 32 oz bottles of Pineapple juice at $2.50 each, Apple Juice at $2.00 each, and Ginger Ale at 1.50 each

Total Bottles purchased 12

Total Cost $22.00

Recipe calls for Ginger Ale to be equal the amount of Pineapple and Apple Juice combined

Let G = Ginger Ale

Let A = Apple Juice

Let P= Pineapple Juice

Equation 1 for Total Bottles

G + A + P = 12

Equation 2 for Total Cost

1.5G + 2.0A + 2.5P = 22.00

And

G = A + P

Substitution for G in Equation 1

A + P + A + P =12

2A + 2P = 12

We can simplify this by dividing both sides by 2 to yield

Equation 1

A + P = 6

Substitution for G in Equation 2

1.5(A + P) + 2.0A + 2.5P =22

1.5A + 1.5P + 2.0A + 2.5 P = 22

This simplifies to

Equation 2

3.5A + 4.0P = 22

Now can use Elimination to solve for P

A + P = 6

3.5A + 4.0P = 22

Multiply Equation 1 by -3.5

-3.5A - 3.5P = -21

3.5A + 4.0P = 22

0.5P = 1

P = 2

We can find G and A

A + P = 6

A = 4

G = 6

Checking

G + A + P = 12

6 + 4 + 2 = 12

1.5G + 2.0A + 2.5P = 22

1.5(6) + 2.0(4) + 2.5(2) = 22

9 + 8 + 5 = 22

I hope you find this useful