Jenson and Gabriel have some money. If Jenson gives $297 to Gabriel, the ratio of their money will be 2 : 5. If Jenson gives $567 to Gabriel, the ratio of their money will be 1: 4. How much does Jenson have?
| |
Case 1 |
Case 2 |
| |
Jenson |
Gabriel |
Jenson |
Gabriel |
| Before |
10 u + $297 |
25 u - $297 |
7 u + $567 |
28 u - $567 |
| Change |
- $297 |
+ $297 |
- $567 |
+ $567 |
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 + 297 = 7 u + 567
10 u - 7 u = 567 - 297
3 u = 270
1 u = 270 ÷ 3 = 90
Amount that Jenson has
= 10 u + 297
= 10 x 90 + 297
= 900 + 297
= $1197
Answer(s): $1197
