Julian and Rael have some money. If Julian gives $361 to Rael, the ratio of their money will be 2 : 5. If Julian gives $613 to Rael, the ratio of their money will be 1: 4. How much does Julian have?
|
Case 1 |
Case 2 |
|
Julian |
Rael |
Julian |
Rael |
Before |
10 u + $361 |
25 u - $361 |
7 u + $613 |
28 u - $613 |
Change |
- $361 |
+ $361 |
- $613 |
+ $613 |
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 Julian has at first is the same in both cases.
10 u + 361 = 7 u + 613
10 u - 7 u = 613 - 361
3 u = 252
1 u = 252 ÷ 3 = 84
Amount that Julian has
= 10 u + 361
= 10 x 84 + 361
= 840 + 361
= $1201
Answer(s): $1201