There were 181 red, silver and blue pens in a box. 5 blue pens were removed from the box and the ratio of the number of red pens to the number of silver pens to the number of blue pens became 2 : 4 : 5. Then some brown pens were added and the ratio of the number of blue pens to the number of brown pens was 5 : 5.
- What was the ratio of the number of red pens to the number of silver pens to the number of blue pens at first?
- How many pens were in the box in the end?
|
Red |
Silver |
Blue |
Brown |
Total |
Before |
2 u |
4 u |
5 u + 5 |
0 |
181 |
Change 1 |
No change |
No change |
- 5 |
|
- 5 |
After 1 |
2 u |
4 u |
5 u |
|
176 |
Change 2 |
No change |
No change |
No change |
+ 5 u |
|
After 2 |
2 u |
4 u |
5 u |
5 u |
|
(a)
Total number of pens at first
= 2 u + 4 u + 5 u + 5
= 11 u + 5
11 u + 5 = 181
11 u = 181 - 5
11 u = 176
1 u = 176 ÷ 11 = 16
Number of red pens at first
= 2 u
= 2 x 16
= 32
Number of silver pens at first
= 4 u
= 4 x 16
= 64
Number of blue pens at first
= 5 u + 5
= 5 x 16 + 5
= 85
At first
Red pens : Silver pens : Blue pens
32 : 64 : 85
(b)
Total number of pens in the box in the end
= 2 u + 4 u + 5 u + 5 u
= 16 u
= 256
Answer(s): (a) 32 : 64 : 85; (b) 256