Ben and Michael have some money. If Ben gives $188 to Michael, the ratio of their money will be 2 : 5. If Ben gives $617 to Michael, the ratio of their money will be 1: 4. How much does Ben have?
| |
Case 1 |
Case 2 |
| |
Ben |
Michael |
Ben |
Michael |
| Before |
10 u + $188 |
25 u - $188 |
7 u + $617 |
28 u - $617 |
| Change |
- $188 |
+ $188 |
- $617 |
+ $617 |
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 Ben has at first is the same in both cases.
10 u + 188 = 7 u + 617
10 u - 7 u = 617 - 188
3 u = 429
1 u = 429 ÷ 3 = 143
Amount that Ben has
= 10 u + 188
= 10 x 143 + 188
= 1430 + 188
= $1618
Answer(s): $1618
