Question

melissa runs a landscaping business. She has equipment and fuel for $343 per month. If she charges $46 for each lawn, how many lawns must she service to make a profit of at least $800 a month?

Answer 1

We can find this by creating a function to represent how many lawns she's mowed.



`f(x) = 46x - 343`

The 46x represents the profit of 46 dollars per month for each lawn mowed and the -343 is the cost of fuel per month to remove it from profit. We now need to set this function to 800, and solve for x.


`800 = 46x - 343`

`1143 = 46x`

`25.58 = x`

Because she can't mow part of a lawn, we need to round to a whole number. Our options are to round down to 25 or round up to 26. Lets start with the lower number first, and see if the profit for that many lawns is over 800.


`f(25) = 46(25) - 343`

`f(25) = 1150 - 343`

`f(25) = 807`

Because 25 is over 800 dollars, we don't need to calculate 26. Therefore, she needs to mow at least 25 lawns to make a profit of at least 800 dollars a month.