Jenson and Reggie have some money. If Jenson gives $122 to Reggie, the ratio of their money will be 2 : 5. If Jenson gives $557 to Reggie, the ratio of their money will be 1: 4. How much does Jenson have?
| |
Case 1 |
Case 2 |
| |
Jenson |
Reggie |
Jenson |
Reggie |
| Before |
10 u + $122 |
25 u - $122 |
7 u + $557 |
28 u - $557 |
| Change |
- $122 |
+ $122 |
- $557 |
+ $557 |
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 Jenson has at first is the same in both cases.
10 u + 122 = 7 u + 557
10 u - 7 u = 557 - 122
3 u = 435
1 u = 435 ÷ 3 = 145
Amount that Jenson has
= 10 u + 122
= 10 x 145 + 122
= 1450 + 122
= $1572
Answer(s): $1572
