Michael bought 52 notebooks and Liam bought 100 notebooks. After Liam used
37 times as many notebooks as Michael, he was left with five times as many notebooks as Michael. How many notebooks did each of them have in the end?
- Michael
- Liam
| |
Make p the same.
(1)x5 = (3) |
Michael
(1) |
Liam
(2) |
| Before |
260 |
52 |
100 |
| Change |
- 35 u |
- 7 u |
- 3 u |
| After |
5 p |
1 p |
5 p |
(a)
52 - 7 u = 1 p --- (1)
100 - 3 u =
5 p --- (2)
(1)
x5
260 - 35 u =
5 p --- (3)
(3) = (2)
100 - 3 u = 260 - 35 u
35 u - 3 u = 260 - 100
32 u = 160
1 u = 160 ÷ 32 = 5
Number of notebooks that Michael had in the end
= 52 - 7 u
= 52 - 7 x 5
= 52 - 35
= 17
(b)
1 p = 17
Number of notebooks that Liam had in the end
= 5 p
= 5 x 17
= 85
Answer(s): (a) 17; (b) 85
