Vincent and Pierre have some money. If Vincent gives $239 to Pierre, the ratio of their money will be 2 : 5. If Vincent gives $683 to Pierre, the ratio of their money will be 1: 4. How much does Vincent have?
|
Case 1 |
Case 2 |
|
Vincent |
Pierre |
Vincent |
Pierre |
Before |
10 u + $239 |
25 u - $239 |
7 u + $683 |
28 u - $683 |
Change |
- $239 |
+ $239 |
- $683 |
+ $683 |
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 Vincent has at first is the same in both cases.
10 u + 239 = 7 u + 683
10 u - 7 u = 683 - 239
3 u = 444
1 u = 444 ÷ 3 = 148
Amount that Vincent has
= 10 u + 239
= 10 x 148 + 239
= 1480 + 239
= $1719
Answer(s): $1719