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Question 1184970: At first, Ali had 1 3/4 times as many stamps as John had and 1 4/5 times as
many stamps as Sam had. Later, John gave 1/12 of his stamps to Sam, and Ali
gave 1/9 of his stamps to Sam. As a result, Sam had 180 stamps in the end.
a) Find the ratio of the number of John’s savings to the number of Sam’s stamps at first.
b) How many stamps did the three boys have altogether?
Found 3 solutions by josgarithmetic, greenestamps, 54929:
Answer by josgarithmetic(39613)   (Show Source):
You can put this solution on YOUR website! ------------------------------------------------
At first, Ali had 1 3/4 times as many stamps as John had and 1 4/5 times as
many stamps as Sam had.
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That much could be said as, John had 4/7 as many as Ali, and Sam had 5/9 as many as Ali.
At First How Many Stamps LATER
Ali A A-A/9
John (4/7)A (4/7)A-(1/12)(4/7)A
Sam (5/9)A (5/9)A+A/9+(1/12)(4/7)A
Note that the last sentence in description means that  , and you can go onward from here.
Answer by greenestamps(13195)  (Show Source):
You can put this solution on YOUR website!
The given information tells us that John had 4/7 as many stamps as Ali and Sam had 5/9 as many as Ali.
I personally would set the problem up for solving without those ugly fractions.
I would use the least common multiple of those denominators (63) to set the problem up like this:
Ali's stamps: 63x
John's stamps: 36x (4/7 as many as Ali)
Sam's stamps: 35x (5/9 as many as Ali)
Then use those starting numbers with the given information:
Ali John Sam
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63x 36x 35x
63x 33x 38x John gave 1/12 of his stamps (3x) to Sam
56x 33x 45x Ali gave 1/9 of his stamps (7x) to Sam
Sam ended up with 180 stamps:
45x=180
x=180/45=4
a) Find the ratio of the number of John's stamps to the number of Sam's stamps at first
ANSWER: 36x:35x = 36:35
b) How many stamps did the three boys have altogether?
ANSWER: 63x+36x+35x=134x=134(4)=536
Answer by 54929(12)  (Show Source):
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