Jade had some staplers, pencils and markers. The ratio of the number of staplers to the number of pencils was 7 : 1. After giving away 15 pencils, the ratio of the number of markers to the number of pencils was 4 : 1. Jade bought another 180 markers. As a result, there were an equal number of staplers and markers. How many pencils did she have at first?
| |
Staplers |
Pencils |
Markers |
| Before |
7 u |
1 u |
|
| Change |
|
- 15 |
|
| After 1 |
|
1 u - 15 |
4 u - 60 |
| Change |
|
|
+ 180 |
| After 2 |
7 u |
1 u - 15 |
4 u + 120 |
Number of pencils after Jade gave away 15 pencils
= 1 u - 15
After Jade gave away 15 pencils, the ratio of the number of markers to the number of pencils became 4 : 1. This means that the number of pencils was 4 times as many as the number of markers.
Number of markers after Jade gave away 15 pencils
= 4 x (1 u - 15)
= 4 u - 60
Number of markers in the end after Jade bought another 180 markers
= 4 u - 60 + 180
= 4 u + 120
Number of staplers and markers in the end is the same.
7 u = 4 u + 1207 u - 4 u = 1203 u = 120
1 u = 120 ÷ 3 = 40
Total numbers of pencils that Jade had at first
= 1 u
= 40
Answer(s): 40
