Abi had some pencils, notebooks and pens. The ratio of the number of pencils to the number of notebooks was 8 : 1. After giving away 15 notebooks, the ratio of the number of pens to the number of notebooks was 5 : 1. Abi bought another 207 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 |
|
- 15 |
|
| After 1 |
|
1 u - 15 |
5 u - 75 |
| Change |
|
|
+ 207 |
| After 2 |
8 u |
1 u - 15 |
5 u + 132 |
Number of notebooks after Abi gave away 15 notebooks
= 1 u - 15
After Abi gave away 15 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 Abi gave away 15 notebooks
= 5 x (1 u - 15)
= 5 u - 75
Number of pens in the end after Abi bought another 207 pens
= 5 u - 75 + 207
= 5 u + 132
Number of pencils and pens in the end is the same.
8 u = 5 u + 1328 u - 5 u = 1323 u = 132
1 u = 132 ÷ 3 = 44
Total numbers of pencils that Abi had at first
= 8 u
= 8 x 44
= 352
Answer(s): 352
