Rael and Julian have some money. If Rael gives $298 to Julian, the ratio of their money will be 2 : 5. If Rael gives $625 to Julian, the ratio of their money will be 1: 4. How much does Rael have?
| |
Case 1 |
Case 2 |
| |
Rael |
Julian |
Rael |
Julian |
| Before |
10 u + $298 |
25 u - $298 |
7 u + $625 |
28 u - $625 |
| Change |
- $298 |
+ $298 |
- $625 |
+ $625 |
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 Rael has at first is the same in both cases.
10 u + 298 = 7 u + 625
10 u - 7 u = 625 - 298
3 u = 327
1 u = 327 ÷ 3 = 109
Amount that Rael has
= 10 u + 298
= 10 x 109 + 298
= 1090 + 298
= $1388
Answer(s): $1388
