Zane and Harry have some money. If Zane gives $356 to Harry, the ratio of their money will be 2 : 5. If Zane gives $500 to Harry, the ratio of their money will be 1: 4. How much does Zane have?
| |
Case 1 |
Case 2 |
| |
Zane |
Harry |
Zane |
Harry |
| Before |
10 u + $356 |
25 u - $356 |
7 u + $500 |
28 u - $500 |
| Change |
- $356 |
+ $356 |
- $500 |
+ $500 |
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 Zane has at first is the same in both cases.
10 u + 356 = 7 u + 500
10 u - 7 u = 500 - 356
3 u = 144
1 u = 144 ÷ 3 = 48
Amount that Zane has
= 10 u + 356
= 10 x 48 + 356
= 480 + 356
= $836
Answer(s): $836
