Gabriel and Jenson have some money. If Gabriel gives $174 to Jenson, the ratio of their money will be 3 : 5. If Gabriel gives $643 to Jenson, the ratio of their money will be 1: 4. How much does Gabriel have?
| |
Case 1 |
Case 2 |
| |
Gabriel |
Jenson |
Gabriel |
Jenson |
| Before |
15 u + $174 |
25 u - $174 |
8 u + $643 |
32 u - $643 |
| Change |
- $174 |
+ $174 |
- $643 |
+ $643 |
After
|
3x5 =
15 u |
5x5 =
25 u |
1x8 =
8 u |
4x8 =
32 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 8 and 5 is 40.
The amount that Gabriel has at first is the same in both cases.
15 u + 174 = 8 u + 643
15 u - 8 u = 643 - 174
7 u = 469
1 u = 469 ÷ 7 = 67
Amount that Gabriel has
= 15 u + 174
= 15 x 67 + 174
= 1005 + 174
= $1179
Answer(s): $1179
