Question

At a bakery, the price of a cake is $9
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.

c−p=9
8c+14p=402

What is the price of a cake?
A.$15.00

B.$27.27

C.$18.27

D.$24.00

Answer 1

To solve for the prices of the cake (c) and the pie (p), we can use the given system of equations:

1. \( c - p = 9 \) (Equation 1)
2. \( 8c + 14p = 402 \) (Equation 2)

First, we can solve Equation 1 for \( c \):

\[
c = p + 9
\]

Now, substitute \( c \) in Equation 2:

\[
8(p + 9) + 14p = 402
\]

Distributing the 8:

\[
8p + 72 + 14p = 402
\]

Combining like terms:

\[
22p + 72 = 402
\]

Now, subtract 72 from both sides:

\[
22p = 330
\]

Next, divide by 22:

\[
p = 15
\]

Now that we have the price of a pie, we can find the price of a cake using Equation 1:

\[
c = p + 9 = 15 + 9 = 24
\]

Thus, the price of a cake is:

\[
\boxed{24.00}
\]

So the answer is \( D. 24.00 \).