Perry and Gabriel have some money. If Perry gives $197 to Gabriel, the ratio of their money will be 3 : 5. If Perry gives $561 to Gabriel, the ratio of their money will be 1: 4. How much does Perry have?
| |
Case 1 |
Case 2 |
| |
Perry |
Gabriel |
Perry |
Gabriel |
| Before |
15 u + $197 |
25 u - $197 |
8 u + $561 |
32 u - $561 |
| Change |
- $197 |
+ $197 |
- $561 |
+ $561 |
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 Perry has at first is the same in both cases.
15 u + 197 = 8 u + 561
15 u - 8 u = 561 - 197
7 u = 364
1 u = 364 ÷ 7 = 52
Amount that Perry has
= 15 u + 197
= 15 x 52 + 197
= 780 + 197
= $977
Answer(s): $977
