David and Archie have some money. If David gives $307 to Archie, the ratio of their money will be 2 : 5. If David gives $520 to Archie, the ratio of their money will be 1: 4. How much does David have?
| |
Case 1 |
Case 2 |
| |
David |
Archie |
David |
Archie |
| Before |
10 u + $307 |
25 u - $307 |
7 u + $520 |
28 u - $520 |
| Change |
- $307 |
+ $307 |
- $520 |
+ $520 |
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 + 307 = 7 u + 520
10 u - 7 u = 520 - 307
3 u = 213
1 u = 213 ÷ 3 = 71
Amount that David has
= 10 u + 307
= 10 x 71 + 307
= 710 + 307
= $1017
Answer(s): $1017
