Last year you mowed grass and shoveled snow for 10 households. You earned $200 per household mowing for the entire season & $180 per household for shoveling the entire season. If you earned a total of $1880 last year, how many households did you mow and shovel for?!
m + s = 10
200 m + 180 s = 1880
solve the system with substitution or elimination
To solve this problem, we can set up a system of equations. Let's denote the number of households you mowed for as "x" and the number of households you shoveled for as "y".
According to the given information, you earned $200 per household for mowing and $180 per household for shoveling. Therefore, the total amount earned from mowing would be 200x, and the total amount earned from shoveling would be 180y.
We also know that the total amount earned last year was $1880. So, we have the equation:
200x + 180y = 1880 ----(1)
Additionally, we know that you mowed grass and shoveled snow for a total of 10 households:
x + y = 10 ----(2)
Now, we can solve this system of equations to find the values of x and y.
From equation (2), we have x = 10 - y. We can substitute this value of x in equation (1):
200(10 - y) + 180y = 1880
Expanding the equation:
2000 - 200y + 180y = 1880
Combining like terms:
-20y = 1880 - 2000
-20y = -120
Dividing both sides of the equation by -20:
y = -120 / -20
y = 6
Now that we have the value of y, we can substitute it back into equation (2) to find the value of x:
x + 6 = 10
x = 10 - 6
x = 4
Therefore, you mowed grass for 4 households and shoveled snow for 6 households last year.