Zane and Liam have some money. If Zane gives $337 to Liam, the ratio of their money will be 3 : 5. If Zane gives $645 to Liam, the ratio of their money will be 1: 4. How much does Zane have?
| |
Case 1 |
Case 2 |
| |
Zane |
Liam |
Zane |
Liam |
| Before |
15 u + $337 |
25 u - $337 |
8 u + $645 |
32 u - $645 |
| Change |
- $337 |
+ $337 |
- $645 |
+ $645 |
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 Zane has at first is the same in both cases.
15 u + 337 = 8 u + 645
15 u - 8 u = 645 - 337
7 u = 308
1 u = 308 ÷ 7 = 44
Amount that Zane has
= 15 u + 337
= 15 x 44 + 337
= 660 + 337
= $997
Answer(s): $997
