Question

(08.06 MC)

Clara and his friends bought cheese wafers for $3 per packet and chocolate wafers for $2 per packet at a carnival. They spent a total of $25 to buy a total of 11 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 Clara and his friends bought at the carnival. Make sure you say what each variable means! (Which one is which wafer type?) (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

A:

Let x = cheese wafers and Y = chocolate

Set up the two equations:

Total packets: x + y = 11

Total cost: 3x + 2y = 25

B: Solve:

Rewrite x+y = 11 as x= 11-y

Replace x in the second equation:

3(11-y) + 2y = 25

Simplify:

33-3y +2y = 25

Combine like terms:

33-y = 25

Subtract 33 from both sides:

-y = -8

Divide both sides by -1:

y = 8

Now replace y in the first equation to solve for x:

x +8 = 11

x = 3

They bought 3 cheese wafers and 8 chocolate wafers.

Used the substitution method, which eliminates one of the variables so you can solve for the second variable.