Erika had some pencils, notebooks and pens. The ratio of the number of pencils to the number of notebooks was 8 : 1. After giving away 17 notebooks, the ratio of the number of pens to the number of notebooks was 5 : 1. Erika bought another 178 pens. As a result, there were an equal number of pencils and pens. How many pencils did she have at first?
| |
Pencils |
Notebooks |
Pens |
| Before |
8 u |
1 u |
|
| Change |
|
- 17 |
|
| After 1 |
|
1 u - 17 |
5 u - 85 |
| Change |
|
|
+ 178 |
| After 2 |
8 u |
1 u - 17 |
5 u + 93 |
Number of notebooks after Erika gave away 17 notebooks
= 1 u - 17
After Erika gave away 17 notebooks, the ratio of the number of pens to the number of notebooks became 5 : 1. This means that the number of notebooks was 5 times as many as the number of pens.
Number of pens after Erika gave away 17 notebooks
= 5 x (1 u - 17)
= 5 u - 85
Number of pens in the end after Erika bought another 178 pens
= 5 u - 85 + 178
= 5 u + 93
Number of pencils and pens in the end is the same.
8 u = 5 u + 938 u - 5 u = 933 u = 93
1 u = 93 ÷ 3 = 31
Total numbers of pencils that Erika had at first
= 8 u
= 8 x 31
= 248
Answer(s): 248
