Diana had some pens, notebooks and pencils. The ratio of the number of pens to the number of notebooks was 7 : 1. After giving away 25 notebooks, the ratio of the number of pencils to the number of notebooks was 5 : 1. Diana bought another 205 pencils. As a result, there were an equal number of pens and pencils. How many pens did she have at first?
| |
Pens |
Notebooks |
Pencils |
| Before |
7 u |
1 u |
|
| Change |
|
- 25 |
|
| After 1 |
|
1 u - 25 |
5 u - 125 |
| Change |
|
|
+ 205 |
| After 2 |
7 u |
1 u - 25 |
5 u + 80 |
Number of notebooks after Diana gave away 25 notebooks
= 1 u - 25
After Diana gave away 25 notebooks, the ratio of the number of pencils to the number of notebooks became 5 : 1. This means that the number of notebooks was 5 times as many as the number of pencils.
Number of pencils after Diana gave away 25 notebooks
= 5 x (1 u - 25)
= 5 u - 125
Number of pencils in the end after Diana bought another 205 pencils
= 5 u - 125 + 205
= 5 u + 80
Number of pens and pencils in the end is the same.
7 u = 5 u + 807 u - 5 u = 802 u = 80
1 u = 80 ÷ 2 = 40
Total numbers of pens that Diana had at first
= 7 u
= 7 x 40
= 280
Answer(s): 280
