Final answer:
By setting up a system of equations and using elimination, we found that Matt earns $4 for each load of laundry and $3 for each load of dishes.
Step-by-step explanation:
The student is asking how to determine how much Matt earns for each type of chore he completed, given the payments he received for different quantities of chores over two weeks. To solve this, we will set up a system of equations based on the information provided.
Let L represent the amount Matt earns for one load of laundry and D represent the amount he earns for one load of dishes. We can write two equations based on the information:
- 6L + 1D = $27
- 1L + 9D = $31
To solve the system, we can use the method of substitution or elimination. Here, I will demonstrate the elimination method:
- Multiply the second equation by 6 so that the coefficients of L in both equations match:
- 6(1L + 9D) = 6($31)
- 6L + 54D = $186
Now subtract the first equation from this new equation:
- (6L + 54D) - (6L + 1D) = $186 - $27
- 53D = $159
- D = $3 (Matt earns $3 for each load of dishes)
Substitute D in any of the original equations:
- 6L + 1($3) = $27
- 6L + $3 = $27
- 6L = $24
- L = $4 (Matt earns $4 for each load of laundry)