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.$18.27

C.$24.00

D.$27.27

We are given two equations:

\[
c - p = 9
\]
\[
8c + 14p = 402
\]

Where:
- $ c $ is the cost of a cake,
- $ p $ is the cost of a pie.

### Step 1: Solve the first equation for $ c $.

From the first equation $ c - p = 9 $, we can solve for $ c $ in terms of $ p $:
\[
c = p + 9
\]

### Step 2: Substitute $ c = p + 9 $ into the second equation.

Substitute the expression for $ c $ into the second equation $ 8c + 14p = 402 $:
\[
8(p + 9) + 14p = 402
\]

### Step 3: Simplify and solve for $ p $.

Distribute the 8:
\[
8p + 72 + 14p = 402
\]
Combine like terms:
\[
22p + 72 = 402
\]
Subtract 72 from both sides:
\[
22p = 330
\]
Solve for $ p $:
\[
p = \frac{330}{22} = 15
\]

### Step 4: Find the price of a cake.

Now that we know $ p = 15 $, substitute this value back into the equation $ c = p + 9 $:
\[
c = 15 + 9 = 24
\]

Thus, the price of a cake is **$24.00**.

The correct answer is **C. $24.00**.

Would you like more details or have any questions? 

Here are 5 related questions:
1. What would be the price of a pie based on this solution?
2. How many cakes would the bakery need to sell to earn $500 if the price of a cake is $24?
3. Can this system of equations be solved using a graphing method? If so, how?
4. How do substitution and elimination methods differ when solving systems of equations?
5. If the price of a pie increases by 10%, what will be the new total revenue from selling 8 cakes and 14 pies?

**Tip:** When solving systems of equations, always check your solution by substituting the values back into the original equations to ensure they satisfy both.

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. $18.27
C. $24.00
D. $27.27

Learn how to solve a system of equations to find the price of a cake at a bakery, given that a cake costs $9 more than a pie. This problem demonstrates how to use the substitution method with linear equations and is suitable for students in Grades 8-10.

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