Problem Analysis:
We are tasked with writing a linear equation in
standard form that models the given word problem. The standard form of a linear equation is:
\[
Ax + By = C
\]
where \( A \), \( B \), and \( C \) are constants, and \( x \) and \( y \) are variables.
#### Given Information:
1. Each CD costs \$10.
2. Each book costs \$6.
3. You want to spend exactly \$32.
4. Let \( c \) represent the number of CDs you buy.
5. Let \( b \) represent the number of books you buy.
Step-by-Step Solution:
#### 1. Define the Variables:
- \( c \): Number of CDs bought.
- \( b \): Number of books bought.
#### 2. Write the Cost Equation:
The total cost of buying \( c \) CDs and \( b \) books is given by:
\[
\text{Total Cost} = (\text{Cost per CD} \times \text{Number of CDs}) + (\text{Cost per Book} \times \text{Number of Books})
\]
Substitute the given values:
\[
\text{Total Cost} = (10 \times c) + (6 \times b)
\]
Since you want to spend exactly \$32, set the total cost equal to 32:
\[
10c + 6b = 32
\]
#### 3. Verify the Standard Form:
The equation \( 10c + 6b = 32 \) is already in standard form, where:
- \( A = 10 \)
- \( B = 6 \)
- \( C = 32 \)
- \( x = c \)
- \( y = b \)
#### 4. Final Answer:
The linear equation in standard form that models the situation is:
\[
\boxed{10c + 6b = 32}
\]
Explanation:
- The equation \( 10c + 6b = 32 \) ensures that the total cost of buying \( c \) CDs and \( b \) books equals \$32.
- This equation can be used to find combinations of \( c \) and \( b \) that satisfy the condition of spending exactly \$32.
Thus, the final answer is:
\[
\boxed{10c + 6b = 32}
\]
Parent Tip: Review the logic above to help your child master the concept of standard form word problems worksheet.
