Ben and Eric have some money. If Ben gives $160 to Eric, the ratio of their money will be 2 : 5. If Ben gives $682 to Eric, the ratio of their money will be 1: 4. How much does Ben have?
| |
Case 1 |
Case 2 |
| |
Ben |
Eric |
Ben |
Eric |
| Before |
10 u + $160 |
25 u - $160 |
7 u + $682 |
28 u - $682 |
| Change |
- $160 |
+ $160 |
- $682 |
+ $682 |
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 + 160 = 7 u + 682
10 u - 7 u = 682 - 160
3 u = 522
1 u = 522 ÷ 3 = 174
Amount that Ben has
= 10 u + 160
= 10 x 174 + 160
= 1740 + 160
= $1900
Answer(s): $1900
