Bryan and Gabriel have some money. If Bryan gives $374 to Gabriel, the ratio of their money will be 3 : 5. If Bryan gives $563 to Gabriel, the ratio of their money will be 1: 4. How much does Bryan have?
| |
Case 1 |
Case 2 |
| |
Bryan |
Gabriel |
Bryan |
Gabriel |
| Before |
15 u + $374 |
25 u - $374 |
8 u + $563 |
32 u - $563 |
| Change |
- $374 |
+ $374 |
- $563 |
+ $563 |
After
|
3x5 =
15 u |
5x5 =
25 u |
1x8 =
8 u |
4x8 =
32 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 8 and 5 is 40.
The amount that Bryan has at first is the same in both cases.
15 u + 374 = 8 u + 563
15 u - 8 u = 563 - 374
7 u = 189
1 u = 189 ÷ 7 = 27
Amount that Bryan has
= 15 u + 374
= 15 x 27 + 374
= 405 + 374
= $779
Answer(s): $779
