the hendersons have just bought a home that requires some monthly yard maintenance. they are trying to…

the 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:\nprofessional service option | do - it - yourself option\n$75 for the first month | $250 lawnmower\n$45 per month after initial visit | $135 edger\nincludes mowing and edging the lawn, trimming the bushes, and raking the leaves. | $69 hedge trimmer\n | $25 rake\nhow long would it take before the hendersons would recover their costs if they chose to do it themselves over the professional service?\n a. 5 months\n b. 9 months\n c. 10 months\n d. 6 months

the 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:\nprofessional service option | do - it - yourself option\n$75 for the first month | $250 lawnmower\n$45 per month after initial visit | $135 edger\nincludes mowing and edging the lawn, trimming the bushes, and raking the leaves. | $69 hedge trimmer\n | $25 rake\nhow long would it take before the hendersons would recover their costs if they chose to do it themselves over the professional service?\n a. 5 months\n b. 9 months\n c. 10 months\n d. 6 months

Answer

Explanation:

Step1: Calculate total DIY cost

The total cost of do - it - yourself option is the sum of the costs of lawnmower, edger, hedge trimmer and rake. So, $250 + 135+69 + 25=479$.

Step2: Set up cost - equation for professional service

Let $n$ be the number of months. The cost of professional service $C_p$ is $75+45(n - 1)$ for $n\geq1$.

Step3: Set up the break - even equation

We want to find $n$ such that the cost of professional service equals the cost of do - it - yourself option. So, $75+45(n - 1)=479$. First, expand the left - hand side: $75+45n-45 = 479$. Simplify to get $30 + 45n=479$. Then, subtract 30 from both sides: $45n=479 - 30=449$. $n=\frac{449}{45}\approx9.98$. Since we are looking for the number of months when the DIY cost is recovered compared to the professional service cost, and we consider whole months, when $n = 10$ months, the DIY cost will be recovered.

Answer:

c. 10 months