Question

Derek had 104 more stamps than Ahmad. Derek then gave 1/9 of his stamps to

Ahmad. In the end, Derek had 4 times as many stamps as Ahmad. How many
stamps did Derek have at first?​

Answer 1

117

Explanation:

Let d represent the number of stamps Derek had at first. After he gave 1/9 of his stamps to Ahmad, Ahmad had (d -104) +(d/9). Derek had 4 times this number after giving away d/9 stamps:

(d -d/9) = 4((d -104) +d/9)

(8/9)d = 4d -416 +(4/9)d

416 = (32/9)d . . . . add 416 -8/9d

117 = d . . . . . . . . . . multiply by 9/32

Derek had 117 stamps at first.

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Check

1/9 of Derek's collection is 13 stamps. 104 less than Derek's collection is 13 stamps.

So, Ahmad started with 13 stamps and was given 13 stamps by Derek. Meanwhile, Derek started with 117 stamps and gave away 13, so ended with 104 stamps. That number (104) is 4 times Ahmad's new number (26), as it should be.