Elijah bought 45 pencils and Howard bought 69 pencils. After Howard used
35 times as many pencils as Elijah, he was left with twice as many pencils as Elijah. How many pencils did each of them have in the end?
- Elijah
- Howard
| |
Make p the same.
(1)x2 = (3) |
Elijah
(1) |
Howard
(2) |
| Before |
90 |
45 |
69 |
| Change |
- 10 u |
- 5 u |
- 3 u |
| After |
2 p |
1 p |
2 p |
(a)
45 - 5 u = 1 p --- (1)
69 - 3 u =
2 p --- (2)
(1)
x2
90 - 10 u =
2 p --- (3)
(3) = (2)
69 - 3 u = 90 - 10 u
10 u - 3 u = 90 - 69
7 u = 21
1 u = 21 ÷ 7 = 3
Number of pencils that Elijah had in the end
= 45 - 5 u
= 45 - 5 x 3
= 45 - 15
= 30
(b)
1 p = 30
Number of pencils that Howard had in the end
= 2 p
= 2 x 30
= 60
Answer(s): (a) 30; (b) 60
