Roshel had 252 pens.
37 were red and the rest were brown and grey. The ratio of the number of brown pens to the number of grey pens was 1 : 5. Roshel decided to buy some more red pens to increase the number of red pens to half of the total number of pens.
- How many less brown pens than red pens did he have at first?
- How many more red pens did he have to buy?
| Red pens |
Brown pens |
Grey pens |
Total |
| 3x3 |
4x3 |
|
| |
1x2 |
5x2 |
|
| 9 u |
2 u |
10 u |
252 |
| |
Red pens |
Brown pens |
Grey pens |
| Before |
9 u |
2 u |
10 u |
| Change |
+ ? |
|
|
| After |
12 u |
12 u |
Comparing red, brown
and grey pens
in the end |
1 |
1 |
(a)
The total number of brown pens and grey pens is repeated. Make the total number of brown pens and grey pens the same. LCM of 4 and 6 is 12.
Total number of pens at first
= 9 u + 2 u + 10 u
= 21 u
21 u = 252
1 u = 252 ÷ 21 = 12
Number of less brown pens than red pens at first
= 9 u - 2 u
= 7 u
= 7 x 12
= 84
(b)
Number of more red pens that Roshel had to buy
= 12 u - 9 u
= 3 u
= 3 x 12
= 36
Answer(s): (a) 84; (b) 36
