Ben and Owen have some money. If Ben gives $370 to Owen, the ratio of their money will be 2 : 5. If Ben gives $664 to Owen, the ratio of their money will be 1: 4. How much does Ben have?
| |
Case 1 |
Case 2 |
| |
Ben |
Owen |
Ben |
Owen |
| Before |
10 u + $370 |
25 u - $370 |
7 u + $664 |
28 u - $664 |
| Change |
- $370 |
+ $370 |
- $664 |
+ $664 |
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 + 370 = 7 u + 664
10 u - 7 u = 664 - 370
3 u = 294
1 u = 294 ÷ 3 = 98
Amount that Ben has
= 10 u + 370
= 10 x 98 + 370
= 980 + 370
= $1350
Answer(s): $1350
