McCoy Max speed, Inc, Makes custom skateboards for its customers. Two wooden skateboards and three composite skateboards cost $650. Three wooden skateboards and one composite skateboards cost $450. How much would McCoy Max speed charge a customer who purchases five wooden skateboards and four composite skateboards?

Options

A. 500
B. 600
C. 1000
D. 1100

Answer

To solve the problem, we need to set up a system of equations based on the information given about the costs of wooden and composite skateboards.

### Step 1: Define Variables
Let:
- \( W \) = cost of one wooden skateboard
- \( C \) = cost of one composite skateboard

### Step 2: Set Up Equations
From the problem, we have the following two equations based on the costs provided:
1. For two wooden skateboards and three composite skateboards costing $650:
\[ 2W + 3C = 650 \quad \text{(Equation 1)} \]
2. For three wooden skateboards and one composite skateboard costing $450:
\[ 3W + 1C = 450 \quad \text{(Equation 2)} \]

### Step 3: Solve the System of Equations
We can solve these two equations simultaneously.

First, let's manipulate Equation 2 to isolate \( C \):
\[ C = 450 - 3W \quad \text{(Substituting into Equation 1)} \]

Now, substitute \( C \) in Equation 1:
\[ 2W + 3(450 - 3W) = 650 \]
Expanding this gives:
\[ 2W + 1350 - 9W = 650 \]
Combining like terms:
\[ -7W + 1350 = 650 \]
Now, isolate \( W \):
\[ -7W = 650 - 1350 \]
\[ -7W = -700 \]
\[ W = 100 \]

### Step 4: Find the Value of \( C \)
Now that we have \( W \), we can substitute it back into Equation 2 to find \( C \):
\[ 3(100) + C = 450 \]
\[ 300 + C = 450 \]
\[ C = 450 - 300 \]
\[ C = 150 \]

### Step 5: Calculate the Total Cost for 5 Wooden and 4 Composite Skateboards
Now we need to find the total cost for 5 wooden skateboards and 4 composite skateboards:
\[ \text{Total Cost} = 5W + 4C \]
Substituting the values of \( W \) and \( C \):
\[ \text{Total Cost} = 5(100) + 4(150) \]
Calculating this gives:
\[ \text{Total Cost} = 500 + 600 = 1100 \]

### Conclusion
Thus, McCoy Max Speed would charge a customer who purchases five wooden skateboards and four composite skateboards **$1100**.

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