Question

he Hendersons have just bought a home that requires some monthly yard maintenance. They are trying to decide if they should hire a professional lawn care service to maintain the property or do it themselves. Below are the costs associated with both options:

Professional Service Option
Do-It-Yourself Option
$75 for the first month
$250 lawnmower
$45 per month after initial visit
$135 edger
Includes mowing and edging the lawn, trimming the bushes, and raking the leaves.
$69 hedge trimmer

$25 rake

How long would it take before the Hendersons would recover their costs if they chose to do it themselves over the professional service?
a.
5 months
b.
9 months
c.
10 months
d.
6 months

Answer 1

Professional cost for n months = 75 + 45(n − 1) = 45n + 30.
DIY upfront cost = 250 + 135 + 69 + 25 = 479.

Set equal: 45n + 30 = 479 → 45n = 449 → n ≈ 9.98, so by the end of the 10th month DIY is cheaper.

Answer: c. 10 months.