Pierre and Gabriel have some money. If Pierre gives $264 to Gabriel, the ratio of their money will be 2 : 5. If Pierre gives $483 to Gabriel, the ratio of their money will be 1: 4. How much does Pierre have?
| |
Case 1 |
Case 2 |
| |
Pierre |
Gabriel |
Pierre |
Gabriel |
| Before |
10 u + $264 |
25 u - $264 |
7 u + $483 |
28 u - $483 |
| Change |
- $264 |
+ $264 |
- $483 |
+ $483 |
After
|
2x5 =
10 u |
5x5 =
25 u |
1x7 =
7 u |
4x7 =
28 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 7 and 5 is 35.
The amount that Pierre has at first is the same in both cases.
10 u + 264 = 7 u + 483
10 u - 7 u = 483 - 264
3 u = 219
1 u = 219 ÷ 3 = 73
Amount that Pierre has
= 10 u + 264
= 10 x 73 + 264
= 730 + 264
= $994
Answer(s): $994
