Ethan and Tommy have some money. If Ethan gives $257 to Tommy, the ratio of their money will be 2 : 5. If Ethan gives $485 to Tommy, the ratio of their money will be 1: 4. How much does Ethan have?
| |
Case 1 |
Case 2 |
| |
Ethan |
Tommy |
Ethan |
Tommy |
| Before |
10 u + $257 |
25 u - $257 |
7 u + $485 |
28 u - $485 |
| Change |
- $257 |
+ $257 |
- $485 |
+ $485 |
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 + 257 = 7 u + 485
10 u - 7 u = 485 - 257
3 u = 228
1 u = 228 ÷ 3 = 76
Amount that Ethan has
= 10 u + 257
= 10 x 76 + 257
= 760 + 257
= $1017
Answer(s): $1017
