Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. Billy gets paid at home for doing extra chores. Last week, he did 4 loads of laundry and 2 loads of dishes, and his parents paid him $10. The week before, he finished 6 loads of laundry and 7 loads of dishes, earning a total of $19. How much does Billy earn for completing each type of chore? Billy earns $_____ per load of laundry and $_____ per load of dishes.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  Billy gets paid at home for doing extra chores. Last week, he did 4 loads of laundry and  2 loads of dishes, and his parents paid him $10. The week before, he finished 6 loads of laundry and  7 loads of dishes, earning a total of $19. How much does Billy earn for completing each type of chore?  Billy earns $_____ per load of laundry and $_____ per load of dishes.

Bytelearn · Accepted Answer

Define earnings per task: Let's denote the amount Billy earns per load of laundry as l and per load of dishes as d. From the first week, we have the equation 4l + 2d = 10. This represents the $10 he earned from 4 loads of laundry and 2 loads of dishes.Formulate system of equations: From the week before, we have the equation 6l + 7d = 19, which represents the $19 he earned from 6 loads of laundry and 7 loads of dishes.Use elimination method: We now have a system of two equations: 1. 4l + 2d = 10 2. 6l + 7d = 19 We will use elimination to solve this system. To eliminate one of the variables, we can multiply the first equation by 3 and the second equation by 2, so the coefficients of l will be the same.Solve for cost of dishes: Multiplying the first equation by 3 gives us 12l + 6d = 30. Multiplying the second equation by 2 gives us 12l + 14d = 38.Substitute and solve for laundry cost: We now subtract the first new equation from the second new equation to eliminate l. This gives us 12l + 14d - (12l + 6d) = 38 - 30, which simplifies to 8d = 8.Dividing both sides of 8d = 8 by 8 gives us d = 1. This means Billy earns $1 per load of dishes.We substitute d = 1 into the first original equation 4l + 2d = 10 and solve for l. This gives us 4l + 2(1) = 10, which simplifies to 4l + 2 = 10.Subtracting 2 from both sides of 4l + 2 = 10 gives us 4l = 8. Dividing both sides by 4 gives us l = 2. This means Billy earns $2 per load of laundry.

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