Question

Mike and his friends bought cheese wafers for $2 per packet and chocolate wafers for $1 per packet at a carnival. They spent a total of $25 to buy a total of 20 packets of wafers of the two varieties.

Part A: Write a system of equations that can be solved to find the number of packets of cheese wafers and the number of packets of chocolate wafers that Mike and his friends bought at the carnival. Define the variables used in the equations. (5 points)

Part B: How many packets of chocolate wafers and cheese wafers did they buy? Explain how you got the answer and why you selected a particular method to get the answer. (5 points)

Answer 1

Part A: 2x + y = 25 and x + y = 20

First equation

2x + y = 25

2x + y + -2 = 25 + -2x

y = -2x + 25

Second equation

x + y = 20

x + -2x + 25 = 20

-x + 25 = 20

-x + 25 + -25 = 20 + -25

-x + -5

-x/-1 = -5/-1

x = 5

Third equation

y = -2x + 5

y = -2(5) + 25

y = 15

Part B: He bought 5 cheese wafers and 15 chocolate wafers. I solved it by doing substitution.

Explanation:

Answer 2

A. 2x+y=25; x+y=20
x represents cheese wafers and y represents chocolate wafers.

B. I will choose elimination since there is y and y. I can multiply one equation by -1 to get y and -y, which cancels out.
2x+y=25
-x-y=-20

Add equations
x=5

Plug x in
5+y=20
y=15

Final answer: 5 cheese wafers, 15 chocolate wafers