Rael and Eric have some money. If Rael gives $125 to Eric, the ratio of their money will be 3 : 5. If Rael gives $629 to Eric, the ratio of their money will be 1: 4. How much does Rael have?
| |
Case 1 |
Case 2 |
| |
Rael |
Eric |
Rael |
Eric |
| Before |
15 u + $125 |
25 u - $125 |
8 u + $629 |
32 u - $629 |
| Change |
- $125 |
+ $125 |
- $629 |
+ $629 |
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 Rael has at first is the same in both cases.
15 u + 125 = 8 u + 629
15 u - 8 u = 629 - 125
7 u = 504
1 u = 504 ÷ 7 = 72
Amount that Rael has
= 15 u + 125
= 15 x 72 + 125
= 1080 + 125
= $1205
Answer(s): $1205
