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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 :

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Step-by-step 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,

[tex]x + y = 22[/tex]

as equation 1.

next we also know,

[tex]150x + 225y = 3900[/tex]

as equation 2.

From here we know we can solve using simultaneous equations.

rearranging equation 1 with y the subject,

[tex]y = 22 - x[/tex]

Substitute this equation into equation 2.

[tex]150x + 225(22 - x) = 3900 \\ 150x + 4950 - 225x = 3900 \\ - 75x + 4950 = 3900 \\ - 75x = 3900 - 4950 \\ - 75x = - 1050 \\ x = - 1050 \div - 75 \\ = 14[/tex]

now substitute x = 14 into equation 1.

[tex]14 + y = 22 \\ y = 22 - 14 \\ = 8[/tex]

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

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