Liam, Elijah and Bobby had a total of 88 pens. The ratio of the number of pens that Elijah had to the number of pens that Bobby had was 4 : 3. After Liam and Elijah each gave away half of their pens, the 3 children had 59 pens left. How many pens did Elijah and Bobby have at first?
| |
Liam |
Elijah |
Bobby |
Total |
| Before |
2 p |
4 u |
3 u |
88 |
| Change |
- 1 p |
- 2 u |
|
- 29 |
| After |
1 p |
2 u |
3 u |
59 |
Total number of pens that Liam and Elijah gave away
= 88 - 59
= 29
1 p + 2 u = 29 --- (1)
1 p + 2 u + 3 u = 59
1 p + 5 u = 59 --- (2)
(2) - (1)
(1 p + 5 u) - (1 p + 2 u) = 59 - 29
5 u - 2 u = 30
3 u = 30
1 u = 30 ÷ 3 = 10
Total number of pens that Elijah and Bobby had at first
= 4 u + 3 u
= 7 u
= 7 x 10
= 70
Answer(s): 70
