A job needs 3 people to work for 2 weeks (10 days). Allison works for all 10 day

Question

A job needs 3 people to work for 2 weeks (10 days). Allison works for all 10 days. Brandon works for the first week and Carlee works for the second week. Don works for 6 days, but then is too sick to work. Ellen takes his place for 3 days, then Fiona does the last day. When the job is finished they are all paid the same amount. At first they could not work out how much each person should have, but then Fiona says: "If Ellen gives $150 to Don, then at least Don will have the right amount." If we have enough information, how much was paid for the whole job, and how much does each person get? If we don't, what's a little bit of information that would let you figure it out? The write up here will be a think-aloud. Show your full, complete thought process for your work towards a solution to the problem. Here are some questions to consider: What did you think you should try?

Explanation / Answer

Answer: Total amount paid for the whole job = $2550 (As shown below); Amount paid to Allison, Brandon, Carlee, Don, Ellen and Fiona is $750, $525, $525, $450, $225 and $75, respectively. (As shown below)

1 job can be completed by 3 people in 2 weeks.

In other words, 1 job can be completed by 3 people in 14 days.

In other words, 1/3rd job can be completed by 1 person in 14 days.

In other words, 1/(3 x 14) = 1/42th part of the job can be completed by 1 person in 1 day.

Suppose the total amount paid is 'p' dollars. Then for each days work, each person gets p/42 dollars.

Since, Allison worked for 10 days he should get 10 days x p/42 per day = 10p/42 dollars.

Similarly, Brandon worked for 7 days he should get 7 days x p/42 per day = 7p/42 dollars.

Carlee worked for 7 days she should get 7 days x p/42 per day= 7p/42 dollars.

Don worked for 6 days he should get 6 days x p/42 per day = 6p/42 dollars.

Ellen worked for 3 days she should get 3 days x p/42 per day = 3p/42 dollars.

Fiona worked for 1 days she should get 1 day x p/42 per day = p/42 dollars.

So, together Allison, Brandon, Carlee, Don, Ellen and Fiona should get (10p/42 + 7p/42 + 7p/42 + 6p/42 + 3p/42 + p/42) = 34p/42 dollars.

Now, each of them were paid equal amounts. Meaning each was paid (34p/42)/6 = 34p/252 dollars

So Don got 34p/252 dollars instead of 6p/42 dollars.

If $150 were to be added to the amount Don got, then at least his amount would be right. Which means:

34p/252 + 150 = 6p/42

34p/252 - 6p/42 = 150

2p/42 = 150

p = 3150

We have already concluded that total amount paid for the whole job is 34p/42. i.e. 34 x 3150 / 42 = $2550

Amount paid to Allison, Brandon, Carlee, Don, Ellen and Fiona is 10p/42, 7p/42, 7p/42, 6p/42, 3p/42 and p/42, respectively. i.e. (10 x 3150/42) = $750, (7 x 3150/42) = $525, (7 x 3150/42) = $525, (6 x 3150/42) = $450, (3 x 3150/42) = $225 and (3150/42) = $75, respectively.

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