There were 182 black, yellow and gold pens in a box. 17 gold pens were removed from the box and the ratio of the number of black pens to the number of yellow pens to the number of gold pens became 3 : 5 : 7. Then some red pens were added and the ratio of the number of gold pens to the number of red pens was 7 : 7.
- What was the ratio of the number of black pens to the number of yellow pens to the number of gold pens at first?
- How many pens were in the box in the end?
|
Black |
Yellow |
Gold |
Red |
Total |
Before |
3 u |
5 u |
7 u + 17 |
0 |
182 |
Change 1 |
No change |
No change |
- 17 |
|
- 17 |
After 1 |
3 u |
5 u |
7 u |
|
165 |
Change 2 |
No change |
No change |
No change |
+ 7 u |
|
After 2 |
3 u |
5 u |
7 u |
7 u |
|
(a)
Total number of pens at first
= 3 u + 5 u + 7 u + 17
= 15 u + 17
15 u + 17 = 182
15 u = 182 - 17
15 u = 165
1 u = 165 ÷ 15 = 11
Number of black pens at first
= 3 u
= 3 x 11
= 33
Number of yellow pens at first
= 5 u
= 5 x 11
= 55
Number of gold pens at first
= 7 u + 17
= 7 x 11 + 17
= 94
At first
Black pens : Yellow pens : Gold pens
33 : 55 : 94
(b)
Total number of pens in the box in the end
= 3 u + 5 u + 7 u + 7 u
= 22 u
= 242
Answer(s): (a) 33 : 55 : 94; (b) 242