Two brothers went to a stamp-collecting exhibit where they wanted to buy some old stamps to add to their collections. On one table Marcus found sets of 12 stamps selling for eight dollars; the stamps could also be bought individually. Julius went to another table that offered 32 stamps for 20 dollars. They too could be purchased individually. On the way home from the exhibit, Marcus remarked that he had spent only two dollars more for his stamps at one than had Julius, who had purchased his stamps at table two. Both boys had purchased the same number of stamps.

How many did each have?

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n*8/12 – 2 = n*20/32

First I’ll reduce each fraction at low as they can go. Marcus gets 3 stamps for $2, Julius gets 8 stamps for $5

Let’s see if I remember my algebra…

x * ($2/3) = x * ($5/8) +2

2/3 = 5/8 + 2/x

2/3 – 5/8 = 2/x

16/24 – 15/24 = 2/x

1/24 = 2/x

x/24 = 2

x = 48. They each have 48 stamps.

I’m tried to be verbose, hoping not to make a mistake :)

Frank, you are today’s winner!

48. On table one, each stamp could be purchased for 66 2/3 cents or 2/3 of one dollar. On table two, each stamp could be purchased for 62 1/2 cents or 5/8 of one dollar, the difference between 2/3 and 5/8 of one dollar is 1/24. 2/3 – 5/8 = 16/24 – 15/24 = 1/24. One-twenty-fourth of one dollar is 4 1/6 cents. Since Marcus purchased two dollars worth of stamps more than Julius, and he paid 4 1/6 cents more for each stamp, divide 200/4 1/6 = 200/25/6 = 200 x 6/25 = 48 stamps.