Olivium had some markers, notebooks and pencils. The ratio of the number of markers to the number of notebooks was 6 : 1. After giving away 29 notebooks, the ratio of the number of pencils to the number of notebooks was 3 : 1. Olivium bought another 180 pencils. As a result, there were an equal number of markers and pencils. How many markers did she have at first?
| |
Markers |
Notebooks |
Pencils |
| Before |
6 u |
1 u |
|
| Change |
|
- 29 |
|
| After 1 |
|
1 u - 29 |
3 u - 87 |
| Change |
|
|
+ 180 |
| After 2 |
6 u |
1 u - 29 |
3 u + 93 |
Number of notebooks after Olivium gave away 29 notebooks
= 1 u - 29
After Olivium gave away 29 notebooks, the ratio of the number of pencils to the number of notebooks became 3 : 1. This means that the number of notebooks was 3 times as many as the number of pencils.
Number of pencils after Olivium gave away 29 notebooks
= 3 x (1 u - 29)
= 3 u - 87
Number of pencils in the end after Olivium bought another 180 pencils
= 3 u - 87 + 180
= 3 u + 93
Number of markers and pencils in the end is the same.
6 u = 3 u + 936 u - 3 u = 933 u = 93
1 u = 93 ÷ 3 = 31
Total numbers of markers that Olivium had at first
= 6 u
= 6 x 31
= 186
Answer(s): 186
