Julian and Riordan have some money. If Julian gives $379 to Riordan, the ratio of their money will be 2 : 5. If Julian gives $643 to Riordan, the ratio of their money will be 1: 4. How much does Julian have?
| |
Case 1 |
Case 2 |
| |
Julian |
Riordan |
Julian |
Riordan |
| Before |
10 u + $379 |
25 u - $379 |
7 u + $643 |
28 u - $643 |
| Change |
- $379 |
+ $379 |
- $643 |
+ $643 |
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 + 379 = 7 u + 643
10 u - 7 u = 643 - 379
3 u = 264
1 u = 264 ÷ 3 = 88
Amount that Julian has
= 10 u + 379
= 10 x 88 + 379
= 880 + 379
= $1259
Answer(s): $1259
