Tim and Archie have some money. If Tim gives $191 to Archie, the ratio of their money will be 2 : 5. If Tim gives $557 to Archie, the ratio of their money will be 1: 4. How much does Tim have?
| |
Case 1 |
Case 2 |
| |
Tim |
Archie |
Tim |
Archie |
| Before |
10 u + $191 |
25 u - $191 |
7 u + $557 |
28 u - $557 |
| Change |
- $191 |
+ $191 |
- $557 |
+ $557 |
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 Tim has at first is the same in both cases.
10 u + 191 = 7 u + 557
10 u - 7 u = 557 - 191
3 u = 366
1 u = 366 ÷ 3 = 122
Amount that Tim has
= 10 u + 191
= 10 x 122 + 191
= 1220 + 191
= $1411
Answer(s): $1411
