Question

Katya wants to earn $1500 this summer by doing yard work. She plans on working 125 hours over the summer.

A. Based on her plan, what is the rate, in dollars per hour, that Katya must charge customers for doing yard work to earn $1500 over the summer? Show or explain how you got your answer.

Katya also wants to enroll in a summer class at a local college. As a result, she will have to work 50 hours less than the total number of hours she had originally planned.

B. What is the rate, in dollars per hour, that Katya must charge customers for doing yard work to still earn $1500? Show or explain how you got your answer.

C. Write an equation that represents the relationship between x, the number of hours Katya will have to work, and y, the rate she must charge customers to earn $1500.

D. Explain how a change in x, the number of hours Katya will have to work, affects y, the rate she will have to charge customers to earn $1500, in your equation from part (c).

Answer 1

Katya's rate per hour for the original 125 hours of work is $12 per hour. If she works 50 hours less, the new rate per hour increases to $20. The equation y = $1500 / x shows the inverse relationship between hours worked (x) and the rate charged (y) to achieve the total earnings goal.

Step-by-step explanation:

To calculate the rate per hour Katya must charge to earn $1500 for the 125 hours she plans to work, we divide the total amount she wants to earn by the total hours of work.

A. The rate per hour = Total earnings / Total hours = $1500 / 125 hours = $12 per hour.

Katya now plans to work 50 hours less.

B. New total hours = Original hours - 50 hours = 125 hours - 50 hours = 75 hours.

The new rate per hour she must charge = Total earnings / New total hours = $1500 / 75 hours = $20 per hour.

C. The equation representing the relationship between x (the number of hours) and y (the rate per hour) is: y = $1500 / x.

D. A change in x affects y inversely. As the number of hours x decreases, the rate y increases, and vice versa, to maintain the total earnings of $1500.

Answer 2

The answer is A!!!!!!

Step-by-step explanation: