Question

Consumer Economics The Strauss family is deciding between two lawn-care services. Green Lawn charges a $49 startup fee, plus $29 per month. Grass Team charges a $25 startup fee, plus $37 a month.Part AIn how many months will both lawn-care services cost the same? monthsPart BWhat will that cost be?$Part CIf the family will use the service for only 6 months, how much will it cost to use Green Lawn? $ Grass Team? $Which is the better option? Type in either Green Lawn or Grass Team

Answer 1

Part A

From the question,

Green lawn charges $49 + $29 per month and

Grass team charges $25 + $37 per month

Let the number of month they will charge the same be x, then in x month, they both will charge

`\begin{gathered} 49+$29$x\text{ and } \\ 25+$37$x \\ \text{For them to charge the same, } \\ 49+$29$x=25+$37$x \end{gathered}`

Solving for x, we have

`\begin{gathered} 49+$29$x=25+$37$x \\ 49-25=37x-29x \\ 24=8x \\ (24)/(8)=(8x)/(8) \\ 3=x \\ x=3 \end{gathered}`

Hence, they will cost the same in 3 months

Part B

The cost will be

`\begin{gathered} 49+29x \\ 49+29*3 \\ 49+87=136\text{ or } \\ 25+37x \\ 25+37*3 \\ 25+111=136 \end{gathered}`

Hence the answer is $136

Part C

If the family use the service for only 6 months, then

For Green Lawn, the cost would be

`\begin{gathered} 49+$29$x \\ x\text{ will be 6 months } \\ 49+29*6 \\ 49+174=223\text{ dollars } \\ \end{gathered}`

Hence, Green Lawn will cost $223

For Grass Team, the cost would be

`\begin{gathered} 25+$37$x \\ x\text{ will be 6 months } \\ 25+$37$*6 \\ 25+$222$=247\text{dollars } \\ \end{gathered}`

Hence Grass Team will cost $247

Hence Green Lawn is a better option, since it is cheaper