There were 196 blue, black and brown notebooks in a box. 16 brown notebooks were removed from the box and the ratio of the number of blue notebooks to the number of black notebooks to the number of brown notebooks became 3 : 2 : 7. Then some yellow notebooks were added and the ratio of the number of brown notebooks to the number of yellow notebooks was 7 : 4.
- What was the ratio of the number of blue notebooks to the number of black notebooks to the number of brown notebooks at first?
- How many notebooks were in the box in the end?
|
Blue |
Black |
Brown |
Yellow |
Total |
Before |
3 u |
2 u |
7 u + 16 |
0 |
196 |
Change 1 |
No change |
No change |
- 16 |
|
- 16 |
After 1 |
3 u |
2 u |
7 u |
|
180 |
Change 2 |
No change |
No change |
No change |
+ 4 u |
|
After 2 |
3 u |
2 u |
7 u |
4 u |
|
(a)
Total number of notebooks at first
= 3 u + 2 u + 7 u + 16
= 12 u + 16
12 u + 16 = 196
12 u = 196 - 16
12 u = 180
1 u = 180 ÷ 12 = 15
Number of blue notebooks at first
= 3 u
= 3 x 15
= 45
Number of black notebooks at first
= 2 u
= 2 x 15
= 30
Number of brown notebooks at first
= 7 u + 16
= 7 x 15 + 16
= 121
At first
Blue notebooks : Black notebooks : Brown notebooks
45 : 30 : 121
(b)
Total number of notebooks in the box in the end
= 3 u + 2 u + 7 u + 4 u
= 16 u
= 240
Answer(s): (a) 45 : 30 : 121; (b) 240