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

Question

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 \( D. 24.00 \).