Pierre and Vincent have some money. If Pierre gives $197 to Vincent, the ratio of their money will be 2 : 5. If Pierre gives $608 to Vincent, the ratio of their money will be 1: 4. How much does Pierre have?
|
Case 1 |
Case 2 |
|
Pierre |
Vincent |
Pierre |
Vincent |
Before |
10 u + $197 |
25 u - $197 |
7 u + $608 |
28 u - $608 |
Change |
- $197 |
+ $197 |
- $608 |
+ $608 |
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 + 197 = 7 u + 608
10 u - 7 u = 608 - 197
3 u = 411
1 u = 411 ÷ 3 = 137
Amount that Pierre has
= 10 u + 197
= 10 x 137 + 197
= 1370 + 197
= $1567
Answer(s): $1567