Ethan and Harry have some money. If Ethan gives $400 to Harry, the ratio of their money will be 2 : 5. If Ethan gives $535 to Harry, the ratio of their money will be 1: 4. How much does Ethan have?
| |
Case 1 |
Case 2 |
| |
Ethan |
Harry |
Ethan |
Harry |
| Before |
10 u + $400 |
25 u - $400 |
7 u + $535 |
28 u - $535 |
| Change |
- $400 |
+ $400 |
- $535 |
+ $535 |
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 Ethan has at first is the same in both cases.
10 u + 400 = 7 u + 535
10 u - 7 u = 535 - 400
3 u = 135
1 u = 135 ÷ 3 = 45
Amount that Ethan has
= 10 u + 400
= 10 x 45 + 400
= 450 + 400
= $850
Answer(s): $850
