Sean, Liam and Ben had a total of 95 pens. The ratio of the number of pens that Liam had to the number of pens that Ben had was 8 : 7. After Sean and Liam each gave away half of their pens, the 3 children had 65 pens left. How many pens did Liam and Ben have at first?
| |
Sean |
Liam |
Ben |
Total |
| Before |
2 p |
8 u |
7 u |
95 |
| Change |
- 1 p |
- 4 u |
|
- 30 |
| After |
1 p |
4 u |
7 u |
65 |
Total number of pens that Sean and Liam gave away
= 95 - 65
= 30
1 p + 4 u = 30 --- (1)
1 p + 4 u + 7 u = 65
1 p + 11 u = 65 --- (2)
(2) - (1)
(1 p + 11 u) - (1 p + 4 u) = 65 - 30
11 u - 4 u = 35
7 u = 35
1 u = 35 ÷ 7 = 5
Total number of pens that Liam and Ben had at first
= 8 u + 7 u
= 15 u
= 15 x 5
= 75
Answer(s): 75
