Question
Keith is a software salesman. Let \( y \) represent his total pay (in dollars). Let \( x \) represent the number of copies of Math is Fun he related by the equation \( y=120 x+1800 \). Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What is the change in Keith's total pay for each copy of Math is Fun he sells? What is Keith's total pay if he doesn't sell any copies of Math is Fun?
Ask by Fitzgerald Lynch. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
For each copy of Math is Fun Keith sells, his total pay increases by \$120. If he doesn't sell any copies, his total pay is \$1800.
Solution
**Step 1: Identify the components of the equation**
The total pay is given by the equation
\[
y = 120x + 1800
\]
where:
- \( x \) is the number of copies of Math is Fun sold,
- \( y \) is the total pay in dollars,
- \( 120 \) is the coefficient of \( x \), and represents the change in total pay per copy sold,
- \( 1800 \) is the constant term, representing the base pay when no copies are sold.
**Step 2: Determine the change in total pay for each copy sold**
The coefficient of \( x \) in the equation is \( 120 \).
Thus, the change in Keith's total pay for each copy of Math is Fun he sells is an **increase of \( 120 \) dollars**.
**Step 3: Determine his total pay when no copies are sold**
To find the total pay when no copies are sold, substitute \( x = 0 \) into the equation:
\[
y = 120(0) + 1800 = 0 + 1800 = 1800
\]
Thus, Keith's total pay when he doesn't sell any copies of Math is Fun is **\( 1800 \) dollars**.
**Answer Summary:**
- The change in total pay for each copy sold is \( +120 \) dollars.
- The total pay if no copies are sold is \( 1800 \) dollars.
Answered by UpStudy AI and reviewed by a Professional Tutor
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The Deep Dive
For each copy of "Math is Fun" that Keith sells, his total pay increases by $120. This means that selling just one more book adds $120 to his overall earnings, making his commission structure quite lucrative! If Keith doesn't sell any copies of "Math is Fun," his total pay would be $1800. This amount represents his base salary, ensuring he has a safety net even when sales are low. So even if he's having a slow month, he still brings home a solid paycheck!