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
[tex]C = 9 + P[/tex]
Cakes sold = 8
Pies sold = 14
[tex]Total = \$402[/tex]
Required
Determine C and P
To represent the cakes and pies sold, we have the following expression
[tex]8C + 14P = 402[/tex]
Substitute 9 + P for C
[tex]8(9+P) + 14P = 402[/tex]
Open the bracket
[tex]72 + 8P + 14P = 402[/tex]
Collect Like Terms
[tex]8P + 14P = 402 - 72[/tex]
[tex]22P= 330[/tex]
Divide both sides by 22
[tex]P = \frac{330}{22}[/tex]
[tex]P = 15[/tex]
Recall that
[tex]C = 9 + P[/tex]
[tex]C = 9 + 15[/tex]
[tex]C = 24[/tex]
Hence, the price of the cake is $24 and the price of the Pie is $15
