Gabriel and Billy have some money. If Gabriel gives $202 to Billy, the ratio of their money will be 2 : 5. If Gabriel gives $577 to Billy, the ratio of their money will be 1: 4. How much does Gabriel have?
|
Case 1 |
Case 2 |
|
Gabriel |
Billy |
Gabriel |
Billy |
Before |
10 u + $202 |
25 u - $202 |
7 u + $577 |
28 u - $577 |
Change |
- $202 |
+ $202 |
- $577 |
+ $577 |
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 Gabriel has at first is the same in both cases.
10 u + 202 = 7 u + 577
10 u - 7 u = 577 - 202
3 u = 375
1 u = 375 ÷ 3 = 125
Amount that Gabriel has
= 10 u + 202
= 10 x 125 + 202
= 1250 + 202
= $1452
Answer(s): $1452