one-dollar coins : fifty-cent coinspokemon wrote:Can someone help me with this ratio problem. Thanks!

Hanson had some one-dollar coins and some fifty-cent coins. The ratio of the number of one-dollar coins to the number of fifty-cent coins he had was 2 : 5. Hanson took 140 fifty-cent coins to the bank and changed these fifty-cent coins for the same value of one-dollar coins. In the end, the number of one-dollar coins to the number of fifty-cent coins he had became 5 : 2. Find the value of the fifty-cent coins Hanson had at first.

2u : 5u

+70 -140

5p : 2p

2u +70 -> 5p ... (1)

5u - 140 -> 2p ... (2)

(1) x 2 : 4u + 140 -> 10p ... (3)

(2) x 5 : 25u - 700 -> 10p ... (4)

(4) - (3) : 21u -> 840

1u -> 40

5u -> 200

200 x $0.50 = $100

Ans $100.