Xavier and David have some money. If Xavier gives $383 to David, the ratio of their money will be 2 : 5. If Xavier gives $653 to David, the ratio of their money will be 1: 4. How much does Xavier have?
| |
Case 1 |
Case 2 |
| |
Xavier |
David |
Xavier |
David |
| Before |
10 u + $383 |
25 u - $383 |
7 u + $653 |
28 u - $653 |
| Change |
- $383 |
+ $383 |
- $653 |
+ $653 |
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 Xavier has at first is the same in both cases.
10 u + 383 = 7 u + 653
10 u - 7 u = 653 - 383
3 u = 270
1 u = 270 ÷ 3 = 90
Amount that Xavier has
= 10 u + 383
= 10 x 90 + 383
= 900 + 383
= $1283
Answer(s): $1283
