Pierre and Rael have some money. If Pierre gives $120 to Rael, the ratio of their money will be 2 : 5. If Pierre gives $651 to Rael, the ratio of their money will be 1: 4. How much does Pierre have?
| |
Case 1 |
Case 2 |
| |
Pierre |
Rael |
Pierre |
Rael |
| Before |
10 u + $120 |
25 u - $120 |
7 u + $651 |
28 u - $651 |
| Change |
- $120 |
+ $120 |
- $651 |
+ $651 |
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 + 120 = 7 u + 651
10 u - 7 u = 651 - 120
3 u = 531
1 u = 531 ÷ 3 = 177
Amount that Pierre has
= 10 u + 120
= 10 x 177 + 120
= 1770 + 120
= $1890
Answer(s): $1890
