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Question 1203170: Alan, Ben, Collin and David bought a gift for their teacher and shared the cost equally. David did not bring any money so the rest of the boys paid for his share first. Collin paid 5/9 of the total paid by Alan and Ben that day. Alan paid $4 more than Ben. When David paid the 3 boys the next day, Collin received $36 from him.
(a) How much is the total of Alan and Ben's share of the gift?
(b) How much did Ben pay towards the gift on the day of shopping?
Found 4 solutions by jekoishun, josgarithmetic, greenestamps, ikleyn:
Answer by jekoishun(6)   (Show Source):
Answer by josgarithmetic(39628) (Show Source):
You can put this solution on YOUR website! Four people, and worded description what each person paid. Try to put this arranged as a table.
FIRSTDAY NEXTDAY
Alan b+4 b+4
Ben b b
Collin (5/9)((b+4)+b) (5/9)((b+4)+b)+36
David 0 gave 36 to Collin
I sense to be missing something somehow, or some piece of data is still needed in the description.
Still too, the first sentence "shared cost equally" is not consistant with the rest of description.
Answer by greenestamps(13206)  (Show Source):
You can put this solution on YOUR website!
There is nothing missing from the description of the problem; and the "equally shared" in the first sentence is NOT inconsistent with the rest of the problem.
On the day of shopping, Collin paid 5/9 as much as Alan and Ben together, and David paid nothing. That means Collin paid 5/14 of the total and Alan and Ben together paid 9/14 of the total.
Let 5x be the amount that Collin paid and 9x be the amount that Alan and Ben together paid. Then the total paid was 14x, making each boy's share 14x/4 = 3.5x.
The $36 that David paid Collin the next day was the excess amount Collin paid above his share, which was 5x-3.5x = 1.5x. So
1.5x = $36
x = $36/1.5 = $24
The amount Collin paid was 5x = $120.
The amount Alan and Ben together paid was 9x = $216.
The total amount paid was 14x = $336.
Alan paid $4 more than Ben; simple algebra or some mental arithmetic show that Ben paid $106 and Alan paid $110.
ANSWERS:
a) Since the total was shared equally 4 ways, the total of Alan's and Ben's shares was half of the total of $336, which is $168.
b) On the day of shopping, the amount Ben paid was $106.
Answer by ikleyn(52866)  (Show Source):
You can put this solution on YOUR website! .
There are two categories of Math problem composers.
One category composers write their problems to teach students on Math.
The other category composers write their problems to prove to all others on how smart these writers are.
The difference is seen from the first glance.
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