Ethan and Howard have some money. If Ethan gives $328 to Howard, the ratio of their money will be 2 : 5. If Ethan gives $454 to Howard, the ratio of their money will be 1: 4. How much does Ethan have?
| |
Case 1 |
Case 2 |
| |
Ethan |
Howard |
Ethan |
Howard |
| Before |
10 u + $328 |
25 u - $328 |
7 u + $454 |
28 u - $454 |
| Change |
- $328 |
+ $328 |
- $454 |
+ $454 |
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 + 328 = 7 u + 454
10 u - 7 u = 454 - 328
3 u = 126
1 u = 126 ÷ 3 = 42
Amount that Ethan has
= 10 u + 328
= 10 x 42 + 328
= 420 + 328
= $748
Answer(s): $748
