Rael and Daniel have some money. If Rael gives $310 to Daniel, the ratio of their money will be 2 : 5. If Rael gives $622 to Daniel, the ratio of their money will be 1: 4. How much does Rael have?
| |
Case 1 |
Case 2 |
| |
Rael |
Daniel |
Rael |
Daniel |
| Before |
10 u + $310 |
25 u - $310 |
7 u + $622 |
28 u - $622 |
| Change |
- $310 |
+ $310 |
- $622 |
+ $622 |
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 + 310 = 7 u + 622
10 u - 7 u = 622 - 310
3 u = 312
1 u = 312 ÷ 3 = 104
Amount that Rael has
= 10 u + 310
= 10 x 104 + 310
= 1040 + 310
= $1350
Answer(s): $1350
