Question

Harold gets paid at home for doing extra chores. Last week, he did 2 loads of laundry and 3 loads of dishes, and his parents paid him $17. The week before, he finished 5 loads of laundry and 10 loads of dishes, earning a total of $50.

Write a system of equations that models the above situation.

A. 3x + 2y = 17
10x + 5y = 50

B. 2x - 3y = 17
5x - 10y = 50

C. 2x + 5y = 17
3x + 10y = 50

D. 2x + 3y = 17
5x + 10y = 50

Answer 1

The correct system of equations to represent Harold's payment for chores is option D, which has the equations 2x + 3y = 17 and 5x + 10y = 50 where x is the payment for laundry and y is the payment for dishes.

Step-by-step explanation:

To model the situation described with a system of equations, we want to use two variables: let x represent the amount paid for doing laundry and let y represent the amount paid for doing dishes. According to the information provided:

• 2 loads of laundry and 3 loads of dishes earned Harold $17.
• 5 loads of laundry and 10 loads of dishes earned him $50.

So, we can translate these situations into two linear equations:

1. 2x + 3y = 17 (from the first week's earnings),
2. 5x + 10y = 50 (from the second week's earnings).

These equations give us a system that can be used to find the values of x and y. Looking at the options given, Option D correctly represents the situation of Harold's chores with the system of equations:

• 2x + 3y = 17,
• 5x + 10y = 50.