There were 147 grey, yellow and red notebooks in a box. 3 red notebooks were removed from the box and the ratio of the number of grey notebooks to the number of yellow notebooks to the number of red notebooks became 2 : 4 : 3. Then some purple notebooks were added and the ratio of the number of red notebooks to the number of purple notebooks was 3 : 5.
- What was the ratio of the number of grey notebooks to the number of yellow notebooks to the number of red notebooks at first?
- How many notebooks were in the box in the end?
|
Grey |
Yellow |
Red |
Purple |
Total |
Before |
2 u |
4 u |
3 u + 3 |
0 |
147 |
Change 1 |
No change |
No change |
- 3 |
|
- 3 |
After 1 |
2 u |
4 u |
3 u |
|
144 |
Change 2 |
No change |
No change |
No change |
+ 5 u |
|
After 2 |
2 u |
4 u |
3 u |
5 u |
|
(a)
Total number of notebooks at first
= 2 u + 4 u + 3 u + 3
= 9 u + 3
9 u + 3 = 147
9 u = 147 - 3
9 u = 144
1 u = 144 ÷ 9 = 16
Number of grey notebooks at first
= 2 u
= 2 x 16
= 32
Number of yellow notebooks at first
= 4 u
= 4 x 16
= 64
Number of red notebooks at first
= 3 u + 3
= 3 x 16 + 3
= 51
At first
Grey notebooks : Yellow notebooks : Red notebooks
32 : 64 : 51
(b)
Total number of notebooks in the box in the end
= 2 u + 4 u + 3 u + 5 u
= 14 u
= 224
Answer(s): (a) 32 : 64 : 51; (b) 224