SOLUTION: 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

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(39615)   (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.
-----------------------------------------------

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(13198)   (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 -------------------- 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): You can put this solution on YOUR website!
Let, Ali has “x” number of stamps
number of stamps Ali had = x

Ali had 1 = stamps as John had i.e., John had stamps as Ali had.
number of stamps John had = x
Ali had 1 = stamps as Sam had i.e Sam had stamps as Ali had
number of stamps Sam had = x
John gave of his stamps to Sam, and Ali gave of his
stamps to Sam. As a result Sam has 180 stamps in the end
x + [x] + [x] = 180
+ + = 180

+ = 180
+ = 180
14x+x/21 = 180
= 180
x = 12 * 21

(a) Ratio of John’s savings : Sam’s stamps at first
x : x
:
36:35
(b) Total stamps = x + x + x
= 252 + (252) + (252)
= 252 + 144 + 140
= 536
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