Question

The Yert family hires a landscaping company for 30 weeks. There are two companies to choose from. Green Lawns charges $2 for the first time they service your lawn, and the price will multiply by a factor of 0. 85 every week thereafter. Green Thumbs charges $350 for the first time they service your lawn, and then charges an additional $30 every week thereafter. At 30 weeks, if the Yert family chooses the company that is cheaper, how much money will they save?

Answer 1

The cost-savings if the Yert Family chooses the cheaper company is: $450.50

How do you determine the cheaper company?

First, we determine the cost of the service of each company. Comparing that will give us an idea of the company whose service is cheaper.

Second, we subtract the lower sum from the higher. This gives us the cost savings by the Yert Family.

Step 1

Expressing the payment plan for Green Lawns, we have:

First week= $2
Second week = (2 + (2*0.85) )  = 3.7

Third week= (3.7 + (2*0.85) ) = 5.4

Using the above cumulative method, we arrive at the series of payments due per week

The series of payment are given as follows:
2 + 3.7 + 5.4+7.1+8.8+10.5+12.2+13.9+15.6+17.3+19+20.7+22.4+24.1+25.8+27.5+29.2+30.9+32.6+34.3+36.0+37.7+39.4+41.1+42.8+44.5+46.2+47.9+49.6

= $799.50

Step 2

Expressing the payment plan for Green Thumbs, we have:

350 + (30*30) = $1,250

Step 3

Hence (assuming they go for Green Lawns) the cost savings will be:

$1,250.00 - $799.50 = $450.50

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