Julian and Xavier have some money. If Julian gives $208 to Xavier, the ratio of their money will be 2 : 5. If Julian gives $691 to Xavier, the ratio of their money will be 1: 4. How much does Julian have?
| |
Case 1 |
Case 2 |
| |
Julian |
Xavier |
Julian |
Xavier |
| Before |
10 u + $208 |
25 u - $208 |
7 u + $691 |
28 u - $691 |
| Change |
- $208 |
+ $208 |
- $691 |
+ $691 |
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 + 208 = 7 u + 691
10 u - 7 u = 691 - 208
3 u = 483
1 u = 483 ÷ 3 = 161
Amount that Julian has
= 10 u + 208
= 10 x 161 + 208
= 1610 + 208
= $1818
Answer(s): $1818
