Ken had 240 pens.
56 were brown and the rest were grey and red. The ratio of the number of grey pens to the number of red pens was 1 : 3. Ken decided to give away some brown pens to decrease the number of brown pens to half of the total number of pens.
- How many more brown pens than grey pens did he have at first?
- How many brown pens did he have to give away?
| Brown pens |
Grey pens |
Red pens |
Total |
| 5x4 |
1x4 |
|
| |
1x1 |
3x1 |
|
| 20 u |
1 u |
3 u |
240 |
| |
Brown pens |
Grey pens |
Red pens |
| Before |
20 u |
1 u |
3 u |
| Change |
- ? |
|
|
| After |
4 u |
4 u |
Comparing brown, grey
and red pens
in the end |
1 |
1 |
(a)
The total number of grey pens and red pens is repeated. Make the total number of grey pens and red pens the same. LCM of 1 and 4 is 4.
Total number of pens at first
= 20 u + 1 u + 3 u
= 24 u
24 u = 240
1 u = 240 ÷ 24 = 10
Number of more brown pens than grey pens at first
= 20 u - 1 u
= 19 u
= 19 x 10
= 190
(b)
Number of more brown pens that Ken had to give away
= 20 u - 4 u
= 16 u
= 16 x 10
= 160
Answer(s): (a) 190; (b) 160
