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Chris and Ed decide to help each other by doing repairs on each other's houses. Chris is a carpenter and Ed is an electrician. Chris does carpentry work on his house as well as on Ed's house. Similarly, Ed does electrical repairs on his house and on Chris's house. When they are all finished they realize that Chris spent 57% of his time on his own house and 43% of his time on Ed's house, and that Ed spent 52% of his time on his own house and 48% of his time on Chris's house. If they originally agreed that the total of the work should amount to $15000, how much money should each get for their work

Answer :

Answer:

Chris gets $7,466.16 for his work.

Ed gets $7,533.83 for his work.

Step-by-step explanation:

Let's first divide the total money for the work equally between both houses.

So there are $7500 worth of work being done on Ed's house, and another $7500 worth of work being on Chris's house.

We will also see how much total time was spent on each house for the work:

Chris's house = Work done by chris + work done by Ed

Chris's house = 57% + 48% = 105%

Ed's house = Work done by Ed + work done by Chris

Ed's house = 52% + 43% = 95%

We should now split the money available for each house between Chris and Ed depending on the amount of work they did. So we will multiply $7500 for each house to the ratio a person worked on them.

This makes Chris's earning to:

Chris's earning = 7500 * (57/105) + 7500 * (43/95) = $ 7,466.16

Ed's earning = 7500 * (48/105) + 7500 * (52/95) = $ 7,533.83

fichoh

Using percentage principle, the amount of money each of Ed and Chris should get for their work is $7533.83 and $7466.17 respectively.

Chris's % time spent :

  • Own house = 57%
  • Ed's house = 43%

Ed's % time spent :

  • Own house = 52%
  • Chris's house = 48%

Ed's house total = 43% + 52% = 95%

Chris's house total = 57% + 48% = 105%

Since Initial split is equal ;

  • $15000 / 2 = $7500

Chris's Earning :

(0.57/1.05 × 7500) + (0.43/0.95 × 7500) = 7466.17

Ed's Earning :

(0.52/0.95 × 7500) + (0.48/1.05 × 7500) = $7533.83

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