Sam, Glen and Henry had a total of 60 pens. The ratio of the number of pens that Glen had to the number of pens that Henry had was 4 : 7. After Sam and Glen each gave away half of their pens, the 3 children had 44 pens left. How many pens did Glen and Henry have at first?
| |
Sam |
Glen |
Henry |
Total |
| Before |
2 p |
4 u |
7 u |
60 |
| Change |
- 1 p |
- 2 u |
|
- 16 |
| After |
1 p |
2 u |
7 u |
44 |
Total number of pens that Sam and Glen gave away
= 60 - 44
= 16
1 p + 2 u = 16 --- (1)
1 p + 2 u + 7 u = 44
1 p + 9 u = 44 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 2 u) = 44 - 16
9 u - 2 u = 28
7 u = 28
1 u = 28 ÷ 7 = 4
Total number of pens that Glen and Henry had at first
= 4 u + 7 u
= 11 u
= 11 x 4
= 44
Answer(s): 44
