There were 265 brown, yellow and white pens in a box. 13 white pens were removed from the box and the ratio of the number of brown pens to the number of yellow pens to the number of white pens became 2 : 3 : 9. Then some blue pens were added and the ratio of the number of white pens to the number of blue pens was 9 : 3.
- What was the ratio of the number of brown pens to the number of yellow pens to the number of white pens at first?
- How many pens were in the box in the end?
|
Brown |
Yellow |
White |
Blue |
Total |
Before |
2 u |
3 u |
9 u + 13 |
0 |
265 |
Change 1 |
No change |
No change |
- 13 |
|
- 13 |
After 1 |
2 u |
3 u |
9 u |
|
252 |
Change 2 |
No change |
No change |
No change |
+ 3 u |
|
After 2 |
2 u |
3 u |
9 u |
3 u |
|
(a)
Total number of pens at first
= 2 u + 3 u + 9 u + 13
= 14 u + 13
14 u + 13 = 265
14 u = 265 - 13
14 u = 252
1 u = 252 ÷ 14 = 18
Number of brown pens at first
= 2 u
= 2 x 18
= 36
Number of yellow pens at first
= 3 u
= 3 x 18
= 54
Number of white pens at first
= 9 u + 13
= 9 x 18 + 13
= 175
At first
Brown pens : Yellow pens : White pens
36 : 54 : 175
(b)
Total number of pens in the box in the end
= 2 u + 3 u + 9 u + 3 u
= 17 u
= 306
Answer(s): (a) 36 : 54 : 175; (b) 306