Pierre and Sam have some money. If Pierre gives $263 to Sam, the ratio of their money will be 2 : 5. If Pierre gives $572 to Sam, the ratio of their money will be 1: 4. How much does Pierre have?
| |
Case 1 |
Case 2 |
| |
Pierre |
Sam |
Pierre |
Sam |
| Before |
10 u + $263 |
25 u - $263 |
7 u + $572 |
28 u - $572 |
| Change |
- $263 |
+ $263 |
- $572 |
+ $572 |
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 + 263 = 7 u + 572
10 u - 7 u = 572 - 263
3 u = 309
1 u = 309 ÷ 3 = 103
Amount that Pierre has
= 10 u + 263
= 10 x 103 + 263
= 1030 + 263
= $1293
Answer(s): $1293
