Ethan and Tim have some money. If Ethan gives $316 to Tim, the ratio of their money will be 3 : 5. If Ethan gives $470 to Tim, the ratio of their money will be 1: 4. How much does Ethan have?
| |
Case 1 |
Case 2 |
| |
Ethan |
Tim |
Ethan |
Tim |
| Before |
15 u + $316 |
25 u - $316 |
8 u + $470 |
32 u - $470 |
| Change |
- $316 |
+ $316 |
- $470 |
+ $470 |
After
|
3x5 =
15 u |
5x5 =
25 u |
1x8 =
8 u |
4x8 =
32 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 8 and 5 is 40.
The amount that Ethan has at first is the same in both cases.
15 u + 316 = 8 u + 470
15 u - 8 u = 470 - 316
7 u = 154
1 u = 154 ÷ 7 = 22
Amount that Ethan has
= 15 u + 316
= 15 x 22 + 316
= 330 + 316
= $646
Answer(s): $646
