Oscar and Tom have some money. If Oscar gives $189 to Tom, the ratio of their money will be 2 : 5. If Oscar gives $678 to Tom, the ratio of their money will be 1: 4. How much does Oscar have?
|
Case 1 |
Case 2 |
|
Oscar |
Tom |
Oscar |
Tom |
Before |
10 u + $189 |
25 u - $189 |
7 u + $678 |
28 u - $678 |
Change |
- $189 |
+ $189 |
- $678 |
+ $678 |
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 Oscar has at first is the same in both cases.
10 u + 189 = 7 u + 678
10 u - 7 u = 678 - 189
3 u = 489
1 u = 489 ÷ 3 = 163
Amount that Oscar has
= 10 u + 189
= 10 x 163 + 189
= 1630 + 189
= $1819
Answer(s): $1819