Betty had some markers, staplers and pencils. The ratio of the number of markers to the number of staplers was 8 : 1. After giving away 18 staplers, the ratio of the number of pencils to the number of staplers was 4 : 1. Betty bought another 176 pencils. As a result, there were an equal number of markers and pencils. How many markers did she have at first?
| |
Markers |
Staplers |
Pencils |
| Before |
8 u |
1 u |
|
| Change |
|
- 18 |
|
| After 1 |
|
1 u - 18 |
4 u - 72 |
| Change |
|
|
+ 176 |
| After 2 |
8 u |
1 u - 18 |
4 u + 104 |
Number of staplers after Betty gave away 18 staplers
= 1 u - 18
After Betty gave away 18 staplers, the ratio of the number of pencils to the number of staplers became 4 : 1. This means that the number of staplers was 4 times as many as the number of pencils.
Number of pencils after Betty gave away 18 staplers
= 4 x (1 u - 18)
= 4 u - 72
Number of pencils in the end after Betty bought another 176 pencils
= 4 u - 72 + 176
= 4 u + 104
Number of markers and pencils in the end is the same.
8 u = 4 u + 1048 u - 4 u = 1044 u = 104
1 u = 104 ÷ 4 = 26
Total numbers of markers that Betty had at first
= 8 u
= 8 x 26
= 208
Answer(s): 208
