Yen had 200 pens.
25 were white and the rest were yellow and blue. The ratio of the number of yellow pens to the number of blue pens was 1 : 3. Yen decided to buy some more white pens to increase the number of white pens to half of the total number of pens.
- How many less yellow pens than white pens did he have at first?
- How many more white pens did he have to buy?
| White pens |
Yellow pens |
Blue pens |
Total |
| 2x4 |
3x4 |
|
| |
1x3 |
3x3 |
|
| 8 u |
3 u |
9 u |
200 |
| |
White pens |
Yellow pens |
Blue pens |
| Before |
8 u |
3 u |
9 u |
| Change |
+ ? |
|
|
| After |
12 u |
12 u |
Comparing white, yellow
and blue pens
in the end |
1 |
1 |
(a)
The total number of yellow pens and blue pens is repeated. Make the total number of yellow pens and blue pens the same. LCM of 3 and 4 is 12.
Total number of pens at first
= 8 u + 3 u + 9 u
= 20 u
20 u = 200
1 u = 200 ÷ 20 = 10
Number of less yellow pens than white pens at first
= 8 u - 3 u
= 5 u
= 5 x 10
= 50
(b)
Number of more white pens that Yen had to buy
= 12 u - 8 u
= 4 u
= 4 x 10
= 40
Answer(s): (a) 50; (b) 40
