Julian and Oscar have some money. If Julian gives $109 to Oscar, the ratio of their money will be 3 : 5. If Julian gives $564 to Oscar, the ratio of their money will be 1: 4. How much does Julian have?
| |
Case 1 |
Case 2 |
| |
Julian |
Oscar |
Julian |
Oscar |
| Before |
15 u + $109 |
25 u - $109 |
8 u + $564 |
32 u - $564 |
| Change |
- $109 |
+ $109 |
- $564 |
+ $564 |
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 Julian has at first is the same in both cases.
15 u + 109 = 8 u + 564
15 u - 8 u = 564 - 109
7 u = 455
1 u = 455 ÷ 7 = 65
Amount that Julian has
= 15 u + 109
= 15 x 65 + 109
= 975 + 109
= $1084
Answer(s): $1084
