Bryan, Xavier and Ivan had a total of 122 erasers. The ratio of the number of erasers that Xavier had to the number of erasers that Ivan had was 6 : 7. After Bryan and Xavier each gave away half of their erasers, the 3 children had 89 erasers left. How many erasers did Xavier and Ivan have in the end?
| |
Bryan |
Xavier |
Ivan |
Total |
| Before |
2 p |
6 u |
7 u |
122 |
| Change |
- 1 p |
- 3 u |
|
- 33 |
| After |
1 p |
3 u |
7 u |
89 |
Total number of erasers that Bryan and Xavier gave away
= 122 - 89
= 33
1 p + 3 u = 33 --- (1)
1 p + 3 u + 7 u = 89
1 p + 10 u = 89 --- (2)
(2) - (1)
(1 p + 10 u) - (1 p + 3 u) = 89 - 33
10 u - 3 u = 56
7 u = 56
1 u = 56 ÷ 7 = 8
Total number of erasers that Xavier and Ivan had in the end
= 3 u + 7 u
= 10 u
= 10 x 8
= 80
Answer(s): 80
