Fabian, Cole and Bobby had a total of 52 erasers. The ratio of the number of erasers that Cole had to the number of erasers that Bobby had was 2 : 3. After Fabian and Cole each gave away half of their erasers, the 3 children had 35 erasers left. How many erasers did Cole and Bobby have at first?
| |
Fabian |
Cole |
Bobby |
Total |
| Before |
2 p |
2 u |
3 u |
52 |
| Change |
- 1 p |
- 1 u |
|
- 17 |
| After |
1 p |
1 u |
3 u |
35 |
Total number of erasers that Fabian and Cole gave away
= 52 - 35
= 17
1 p + 1 u = 17 --- (1)
1 p + 1 u + 3 u = 35
1 p + 4 u = 35 --- (2)
(2) - (1)
(1 p + 4 u) - (1 p + 1 u) = 35 - 17
4 u - 1 u = 18
3 u = 18
1 u = 18 ÷ 3 = 6
Total number of erasers that Cole and Bobby had at first
= 2 u + 3 u
= 5 u
= 5 x 6
= 30
Answer(s): 30
