David and Pierre have some money. If David gives $337 to Pierre, the ratio of their money will be 2 : 5. If David gives $472 to Pierre, the ratio of their money will be 1: 4. How much does David have?
| |
Case 1 |
Case 2 |
| |
David |
Pierre |
David |
Pierre |
| Before |
10 u + $337 |
25 u - $337 |
7 u + $472 |
28 u - $472 |
| Change |
- $337 |
+ $337 |
- $472 |
+ $472 |
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 David has at first is the same in both cases.
10 u + 337 = 7 u + 472
10 u - 7 u = 472 - 337
3 u = 135
1 u = 135 ÷ 3 = 45
Amount that David has
= 10 u + 337
= 10 x 45 + 337
= 450 + 337
= $787
Answer(s): $787
