There were 134 black, green and gold pens in a box. 8 gold pens were removed from the box and the ratio of the number of black pens to the number of green pens to the number of gold pens became 4 : 5 : 9. Then some blue pens were added and the ratio of the number of gold pens to the number of blue pens was 9 : 3.
- What was the ratio of the number of black pens to the number of green pens to the number of gold pens at first?
- How many pens were in the box in the end?
|
Black |
Green |
Gold |
Blue |
Total |
Before |
4 u |
5 u |
9 u + 8 |
0 |
134 |
Change 1 |
No change |
No change |
- 8 |
|
- 8 |
After 1 |
4 u |
5 u |
9 u |
|
126 |
Change 2 |
No change |
No change |
No change |
+ 3 u |
|
After 2 |
4 u |
5 u |
9 u |
3 u |
|
(a)
Total number of pens at first
= 4 u + 5 u + 9 u + 8
= 18 u + 8
18 u + 8 = 134
18 u = 134 - 8
18 u = 126
1 u = 126 ÷ 18 = 7
Number of black pens at first
= 4 u
= 4 x 7
= 28
Number of green pens at first
= 5 u
= 5 x 7
= 35
Number of gold pens at first
= 9 u + 8
= 9 x 7 + 8
= 71
At first
Black pens : Green pens : Gold pens
28 : 35 : 71
(b)
Total number of pens in the box in the end
= 4 u + 5 u + 9 u + 3 u
= 21 u
= 147
Answer(s): (a) 28 : 35 : 71; (b) 147