Ratio and Proportion

Question

1.If Gary gives $40 to Charles, they will have an equal amount of money. If Charles gave $80 to Gary, the ratio of Gary's money to Charles money will be 4:1. How much money does Gary have at first?

2.If 25 marbles were moved from box A to box B, there would be an equal number of marbles in both boxes. If 100 marbles were moved from Box B to Box A, the ratio of the number of marbles in Box A to those in Box B would be 7:2. What was the original number of marbles in box A?

Answer 1

We have two unknowns: Gary's amount and Charles' amount.

Call Gary's amount g and Charles' amount c both in dollars.

If Gary gives $40 to Charles, their amounts will be the same. Therefore, g - 40 = c + 40

Therefore, c = g - 80

Next, (g + 80)/ (c - 80) = 4/1.

So, g+ 80 = 4(c - 80)

Substitute g - 80 in for c

g + 80 = 4( (g - 80) - 80)

g + 80 = 4(g - 160)

g + 80 = 4g - 640

g + 720 = 4g

720 = 3g

g = 240

Answer 2

Hello, Eiijhay,

Following the same logic as Michael had in his answer to the first part, we can define the relationship between the marbles (A) in box and (B) in Box B. Transferring 25 from A to B makes the same number of marbles in both boxes. When adding 100 marbles to box A from B, the ratio is 7:2. Rearrange the first equation to define A = B + 50, and substitute that into the second equation to find B, which is 200. Since A = B + 50, A is 250 marbles.

Bob