At a bakery, the price of a cake is $9$9 more than the price of a pie. One day, the bakery sold 88 cakes and 1414 pies for a total of $402$402. The system of equations below can be used to find cc, the cost in dollars of a cake, and pp, 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 the system of equations:

\[
c - p = 9 \quad \text{(1)}
\]
\[
8c + 14p = 402 \quad \text{(2)}
\]

We want to find the price of a cake, represented by $ c $.

### Step 1: Solve for $ p $ in terms of $ c $
From equation (1):
\[
c - p = 9
\]
Rearrange this to express $ p $ in terms of $ c $:
\[
p = c - 9
\]

### Step 2: Substitute $ p = c - 9 $ into equation (2)
Now substitute $ p = c - 9 $ into equation (2):
\[
8c + 14(c - 9) = 402
\]

### Step 3: Expand and solve for $ c $
Distribute the 14 on the left side:
\[
8c + 14c - 126 = 402
\]
Combine like terms:
\[
22c - 126 = 402
\]
Add 126 to both sides:
\[
22c = 528
\]
Solve for $ c $:
\[
c = \frac{528}{22} = 24
\]

Thus, the price of a cake is $ c = 24 $.

### Answer:
The price of a cake is **$24.00** (Option C).

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the price of pies be calculated from this system of equations?
2. How does substituting values into one equation simplify the system-solving process?
3. What would happen if the price difference was not a fixed amount but a percentage?
4. Can this system of equations be solved using matrices? If so, how?
5. How does this system of equations change if different quantities of cakes and pies are sold?

**Tip**: When solving a system of equations, always look for ways to simplify one equation using the other—this makes the problem more manageable.

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 linear equations to find the price of a cake and a pie at a bakery. This problem involves setting up two equations and solving for the cost of each item. Suitable for Grades 8-10 students.

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