Ian and Mark have some money. If Ian gives $302 to Mark, the ratio of their money will be 2 : 5. If Ian gives $545 to Mark, the ratio of their money will be 1: 4. How much does Ian have?
|
Case 1 |
Case 2 |
|
Ian |
Mark |
Ian |
Mark |
Before |
10 u + $302 |
25 u - $302 |
7 u + $545 |
28 u - $545 |
Change |
- $302 |
+ $302 |
- $545 |
+ $545 |
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 Ian has at first is the same in both cases.
10 u + 302 = 7 u + 545
10 u - 7 u = 545 - 302
3 u = 243
1 u = 243 ÷ 3 = 81
Amount that Ian has
= 10 u + 302
= 10 x 81 + 302
= 810 + 302
= $1112
Answer(s): $1112