Ben and Ivan have some money. If Ben gives $310 to Ivan, the ratio of their money will be 3 : 5. If Ben gives $562 to Ivan, the ratio of their money will be 1: 4. How much does Ben have?
| |
Case 1 |
Case 2 |
| |
Ben |
Ivan |
Ben |
Ivan |
| Before |
15 u + $310 |
25 u - $310 |
8 u + $562 |
32 u - $562 |
| Change |
- $310 |
+ $310 |
- $562 |
+ $562 |
After
|
3x5 =
15 u |
5x5 =
25 u |
1x8 =
8 u |
4x8 =
32 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 8 and 5 is 40.
The amount that Ben has at first is the same in both cases.
15 u + 310 = 8 u + 562
15 u - 8 u = 562 - 310
7 u = 252
1 u = 252 ÷ 7 = 36
Amount that Ben has
= 15 u + 310
= 15 x 36 + 310
= 540 + 310
= $850
Answer(s): $850
