Question

A bakery the price of the cake is nine dollars more than the price of a pie. One day the bakery sold 8 cakes and 14 pies for a total of $402. The system of equations below can be used to find c the cost in dollars of a cake and P the cost in dollars of a pie. What is the price of a cake?

Answer 1

Answer:

The price of the cake is $24 and the price of the Pie is $15

Step-by-step explanation:

Given

Represent price of Cake with C and Price of Pie with P

$C = 9 + P$

Cakes sold = 8

Pies sold = 14

$Total = \ 402$

Required

Determine C and P

To represent the cakes and pies sold, we have the following expression

$8C + 14P = 402$

Substitute 9 + P for C

$8(9+P) + 14P = 402$

Open the bracket

$72 + 8P + 14P = 402$

Collect Like Terms

$8P + 14P = 402 - 72$

$22P= 330$

Divide both sides by 22

$P = \frac{330}{22}$

$P = 15$

Recall that

$C = 9 + P$

$C = 9 + 15$

$C = 24$

Hence, the price of the cake is $24 and the price of the Pie is $15