Glen, Ben and Jenson had a total of 82 pens. The ratio of the number of pens that Ben had to the number of pens that Jenson had was 6 : 7. After Glen and Ben each gave away half of their pens, the 3 children had 62 pens left. How many pens did Ben and Jenson have at first?
| |
Glen |
Ben |
Jenson |
Total |
| Before |
2 p |
6 u |
7 u |
82 |
| Change |
- 1 p |
- 3 u |
|
- 20 |
| After |
1 p |
3 u |
7 u |
62 |
Total number of pens that Glen and Ben gave away
= 82 - 62
= 20
1 p + 3 u = 20 --- (1)
1 p + 3 u + 7 u = 62
1 p + 10 u = 62 --- (2)
(2) - (1)
(1 p + 10 u) - (1 p + 3 u) = 62 - 20
10 u - 3 u = 42
7 u = 42
1 u = 42 ÷ 7 = 6
Total number of pens that Ben and Jenson had at first
= 6 u + 7 u
= 13 u
= 13 x 6
= 78
Answer(s): 78
