Tom and Sean have some money. If Tom gives $282 to Sean, the ratio of their money will be 2 : 5. If Tom gives $477 to Sean, the ratio of their money will be 1: 4. How much does Tom have?
| |
Case 1 |
Case 2 |
| |
Tom |
Sean |
Tom |
Sean |
| Before |
10 u + $282 |
25 u - $282 |
7 u + $477 |
28 u - $477 |
| Change |
- $282 |
+ $282 |
- $477 |
+ $477 |
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 Tom has at first is the same in both cases.
10 u + 282 = 7 u + 477
10 u - 7 u = 477 - 282
3 u = 195
1 u = 195 ÷ 3 = 65
Amount that Tom has
= 10 u + 282
= 10 x 65 + 282
= 650 + 282
= $932
Answer(s): $932
