Archie, Ken and Owen had a total of 159 pens. The ratio of the number of pens that Ken had to the number of pens that Owen had was 8 : 5. After Archie and Ken each gave away half of their pens, the 3 children had 107 pens left. How many pens did Ken and Owen have at first?
| |
Archie |
Ken |
Owen |
Total |
| Before |
2 p |
8 u |
5 u |
159 |
| Change |
- 1 p |
- 4 u |
|
- 52 |
| After |
1 p |
4 u |
5 u |
107 |
Total number of pens that Archie and Ken gave away
= 159 - 107
= 52
1 p + 4 u = 52 --- (1)
1 p + 4 u + 5 u = 107
1 p + 9 u = 107 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 4 u) = 107 - 52
9 u - 4 u = 55
5 u = 55
1 u = 55 ÷ 5 = 11
Total number of pens that Ken and Owen had at first
= 8 u + 5 u
= 13 u
= 13 x 11
= 143
Answer(s): 143
