There were 131 brown, black and pink pencils in a box. 21 pink pencils were removed from the box and the ratio of the number of brown pencils to the number of black pencils to the number of pink pencils became 4 : 2 : 5. Then some silver pencils were added and the ratio of the number of pink pencils to the number of silver pencils was 5 : 6.
- What was the ratio of the number of brown pencils to the number of black pencils to the number of pink pencils at first?
- How many pencils were in the box in the end?
|
Brown |
Black |
Pink |
Silver |
Total |
Before |
4 u |
2 u |
5 u + 21 |
0 |
131 |
Change 1 |
No change |
No change |
- 21 |
|
- 21 |
After 1 |
4 u |
2 u |
5 u |
|
110 |
Change 2 |
No change |
No change |
No change |
+ 6 u |
|
After 2 |
4 u |
2 u |
5 u |
6 u |
|
(a)
Total number of pencils at first
= 4 u + 2 u + 5 u + 21
= 11 u + 21
11 u + 21 = 131
11 u = 131 - 21
11 u = 110
1 u = 110 ÷ 11 = 10
Number of brown pencils at first
= 4 u
= 4 x 10
= 40
Number of black pencils at first
= 2 u
= 2 x 10
= 20
Number of pink pencils at first
= 5 u + 21
= 5 x 10 + 21
= 71
At first
Brown pencils : Black pencils : Pink pencils
40 : 20 : 71
(b)
Total number of pencils in the box in the end
= 4 u + 2 u + 5 u + 6 u
= 17 u
= 170
Answer(s): (a) 40 : 20 : 71; (b) 170