Question

Last year you mowed grass and shoveled snow for 22 households.

You earned $150 per household mowing for the entire season and $225 per household shoveling the entire season.

If you earned a total of $3900 last year, how many households did you mow and shovel for last year?​

Answer 1

Explanation:

Let x be the number of households you mowed grass.

Let y be the number of households you shoveled snow.

From there, we know,

`x + y = 22`

as equation 1.

next we also know,

`150x + 225y = 3900`

as equation 2.

From here we know we can solve using simultaneous equations.

rearranging equation 1 with y the subject,

`y = 22 - x`

Substitute this equation into equation 2.

`150x + 225(22 - x) = 3900 \\ 150x + 4950 - 225x = 3900 \\ - 75x + 4950 = 3900 \\ - 75x = 3900 - 4950 \\ - 75x = - 1050 \\ x = - 1050 / - 75 \\ = 14`

now substitute x = 14 into equation 1.

`14 + y = 22 \\ y = 22 - 14 \\ = 8`

Therefore, you have mowed grass for 14 households and shovelled snow for 8 households.