Lilian bought 33 pencils and Carl bought 42 pencils. After Carl used
27 times as many pencils as Lilian, he was left with thrice as many pencils as Lilian. How many pencils did each of them have in the end?
- Lilian
- Carl
| |
Make p the same.
(1)x3 = (3) |
Lilian
(1) |
Carl
(2) |
| Before |
99 |
33 |
42 |
| Change |
- 21 u |
- 7 u |
- 2 u |
| After |
3 p |
1 p |
3 p |
(a)
33 - 7 u = 1 p --- (1)
42 - 2 u =
3 p --- (2)
(1)
x3
99 - 21 u =
3 p --- (3)
(3) = (2)
42 - 2 u = 99 - 21 u
21 u - 2 u = 99 - 42
19 u = 57
1 u = 57 ÷ 19 = 3
Number of pencils that Lilian had in the end
= 33 - 7 u
= 33 - 7 x 3
= 33 - 21
= 12
(b)
1 p = 12
Number of pencils that Carl had in the end
= 3 p
= 3 x 12
= 36
Answer(s): (a) 12; (b) 36
