Owen and Mark have some money. If Owen gives $326 to Mark, the ratio of their money will be 2 : 5. If Owen gives $542 to Mark, the ratio of their money will be 1: 4. How much does Owen have?
|
Case 1 |
Case 2 |
|
Owen |
Mark |
Owen |
Mark |
Before |
10 u + $326 |
25 u - $326 |
7 u + $542 |
28 u - $542 |
Change |
- $326 |
+ $326 |
- $542 |
+ $542 |
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 Owen has at first is the same in both cases.
10 u + 326 = 7 u + 542
10 u - 7 u = 542 - 326
3 u = 216
1 u = 216 ÷ 3 = 72
Amount that Owen has
= 10 u + 326
= 10 x 72 + 326
= 720 + 326
= $1046
Answer(s): $1046