There were 199 yellow, red and gold pens in a box. 17 gold pens were removed from the box and the ratio of the number of yellow pens to the number of red pens to the number of gold pens became 4 : 3 : 7. Then some blue pens were added and the ratio of the number of gold pens to the number of blue pens was 7 : 9.
- What was the ratio of the number of yellow pens to the number of red pens to the number of gold pens at first?
- How many pens were in the box in the end?
|
Yellow |
Red |
Gold |
Blue |
Total |
Before |
4 u |
3 u |
7 u + 17 |
0 |
199 |
Change 1 |
No change |
No change |
- 17 |
|
- 17 |
After 1 |
4 u |
3 u |
7 u |
|
182 |
Change 2 |
No change |
No change |
No change |
+ 9 u |
|
After 2 |
4 u |
3 u |
7 u |
9 u |
|
(a)
Total number of pens at first
= 4 u + 3 u + 7 u + 17
= 14 u + 17
14 u + 17 = 199
14 u = 199 - 17
14 u = 182
1 u = 182 ÷ 14 = 13
Number of yellow pens at first
= 4 u
= 4 x 13
= 52
Number of red pens at first
= 3 u
= 3 x 13
= 39
Number of gold pens at first
= 7 u + 17
= 7 x 13 + 17
= 108
At first
Yellow pens : Red pens : Gold pens
52 : 39 : 108
(b)
Total number of pens in the box in the end
= 4 u + 3 u + 7 u + 9 u
= 23 u
= 299
Answer(s): (a) 52 : 39 : 108; (b) 299