Simon and Ethan have some money. If Simon gives $126 to Ethan, the ratio of their money will be 2 : 5. If Simon gives $558 to Ethan, the ratio of their money will be 1: 4. How much does Simon have?
| |
Case 1 |
Case 2 |
| |
Simon |
Ethan |
Simon |
Ethan |
| Before |
10 u + $126 |
25 u - $126 |
7 u + $558 |
28 u - $558 |
| Change |
- $126 |
+ $126 |
- $558 |
+ $558 |
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 Simon has at first is the same in both cases.
10 u + 126 = 7 u + 558
10 u - 7 u = 558 - 126
3 u = 432
1 u = 432 ÷ 3 = 144
Amount that Simon has
= 10 u + 126
= 10 x 144 + 126
= 1440 + 126
= $1566
Answer(s): $1566
