There were 252 pink, brown and gold markers in a box. 14 gold markers were removed from the box and the ratio of the number of pink markers to the number of brown markers to the number of gold markers became 5 : 2 : 7. Then some purple markers were added and the ratio of the number of gold markers to the number of purple markers was 7 : 2.
- What was the ratio of the number of pink markers to the number of brown markers to the number of gold markers at first?
- How many markers were in the box in the end?
|
Pink |
Brown |
Gold |
Purple |
Total |
Before |
5 u |
2 u |
7 u + 14 |
0 |
252 |
Change 1 |
No change |
No change |
- 14 |
|
- 14 |
After 1 |
5 u |
2 u |
7 u |
|
238 |
Change 2 |
No change |
No change |
No change |
+ 2 u |
|
After 2 |
5 u |
2 u |
7 u |
2 u |
|
(a)
Total number of markers at first
= 5 u + 2 u + 7 u + 14
= 14 u + 14
14 u + 14 = 252
14 u = 252 - 14
14 u = 238
1 u = 238 ÷ 14 = 17
Number of pink markers at first
= 5 u
= 5 x 17
= 85
Number of brown markers at first
= 2 u
= 2 x 17
= 34
Number of gold markers at first
= 7 u + 14
= 7 x 17 + 14
= 133
At first
Pink markers : Brown markers : Gold markers
85 : 34 : 133
(b)
Total number of markers in the box in the end
= 5 u + 2 u + 7 u + 2 u
= 16 u
= 272
Answer(s): (a) 85 : 34 : 133; (b) 272