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

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

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 = (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