Find out how many stamps were giving away

Question

Amanda and betty has a total of 3580 stamps at first.

Amanda gave 2/3 of her stamps away and betty bought 20 more

If amanda were to sell 1/3 of her stamps to betty

Amanda would be left with half as many stamps as betty

How many stamps did amanda give away?

Answer 1

Amanda gave away 1,800 stamps in total.

Since Amanda and Betty collectively have 3,580 stamps in total, we can let A = Amanda and B = Betty so that A + B = 3580. In the problem itself, Amanda has half of the number of stamps as Betty if she gives away 2/3 of her initial number of stamps and sold 1/3 of the resulting amount to Betty and if Betty bought 20 more stamps. As a result, we can create the following equation from this scenario:

(A - (2/3)A) - (1/3)(A - (2/3)A) = (1/2)[B + 20 + (1/3)(A - (2/3)A]

A = 3(B + 20)

A = 3B + 60

Then, we can solve this system of equation to find the amount of stamps Betty and Amanda had initially. First, we can plug in A = 3B + 60 into A + B = 3580 so that (3B + 60) + B = 3580, where we find that B = 880. Then, by plugging the value of B into A + B = 3580, we find that A = 2700.

Since Amanda actually did give away 2/3 of her initial number of stamps, but did not actually sell 1/3 of the resulting amount to Betty, Amanda gave away (2/3)(2700) stamps, which is 1,800 stamps.