Yoko had some notebooks, markers and pens. The ratio of the number of notebooks to the number of markers was 6 : 1. After giving away 23 markers, the ratio of the number of pens to the number of markers was 3 : 1. Yoko bought another 219 pens. As a result, there were an equal number of notebooks and pens. How many notebooks did she have at first?
| |
Notebooks |
Markers |
Pens |
| Before |
6 u |
1 u |
|
| Change |
|
- 23 |
|
| After 1 |
|
1 u - 23 |
3 u - 69 |
| Change |
|
|
+ 219 |
| After 2 |
6 u |
1 u - 23 |
3 u + 150 |
Number of markers after Yoko gave away 23 markers
= 1 u - 23
After Yoko gave away 23 markers, the ratio of the number of pens to the number of markers became 3 : 1. This means that the number of markers was 3 times as many as the number of pens.
Number of pens after Yoko gave away 23 markers
= 3 x (1 u - 23)
= 3 u - 69
Number of pens in the end after Yoko bought another 219 pens
= 3 u - 69 + 219
= 3 u + 150
Number of notebooks and pens in the end is the same.
6 u = 3 u + 1506 u - 3 u = 1503 u = 150
1 u = 150 ÷ 3 = 50
Total numbers of notebooks that Yoko had at first
= 6 u
= 6 x 50
= 300
Answer(s): 300
