Math Problem Statement
Nate’s weekly pay, in dollars, when he works x hours is represented by this expression.
{ 16 . 50 x 0 ≤ x ≤ 40 24 . 75 ( x − 40 ) + 660 x
40 16 . 50 x 0≤x≤40 24 . 75 ( x-40 )+660 x>40 How much is Nate paid for each hour he works over 40? A. $8.25
B.
$41.25
C.
$24.75
D.
$16.50
Solution
Nate's pay for each hour over 40 is represented by the second part of the expression:
This tells us that for every hour worked over 40, Nate earns $24.75 per hour, which corresponds to option C.
Answer: C. $24.75
Do you want further details or explanations?
Here are five questions related to the problem:
- How is Nate's pay calculated if he works exactly 40 hours?
- What is the total weekly pay if Nate works 45 hours?
- Why does Nate earn more per hour after 40 hours of work?
- How can we express Nate's weekly pay using a piecewise function?
- What is the interpretation of the $660 term in the expression?
Tip: In piecewise functions, different formulas apply for different conditions (like hours worked), so it's essential to evaluate the correct part based on the value of the variable.
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Linear Equations
Hourly Pay Calculation
Formulas
16.50x for 0 ≤ x ≤ 40
24.75(x - 40) + 660 for x > 40
Theorems
Piecewise Function Evaluation
Suitable Grade Level
Grades 7-9
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