Tammy had some markers, staplers and pens. The ratio of the number of markers to the number of staplers was 7 : 1. After giving away 24 staplers, the ratio of the number of pens to the number of staplers was 5 : 1. Tammy bought another 192 pens. As a result, there were an equal number of markers and pens. How many staplers did she have at first?
| |
Markers |
Staplers |
Pens |
| Before |
7 u |
1 u |
|
| Change |
|
- 24 |
|
| After 1 |
|
1 u - 24 |
5 u - 120 |
| Change |
|
|
+ 192 |
| After 2 |
7 u |
1 u - 24 |
5 u + 72 |
Number of staplers after Tammy gave away 24 staplers
= 1 u - 24
After Tammy gave away 24 staplers, the ratio of the number of pens to the number of staplers became 5 : 1. This means that the number of staplers was 5 times as many as the number of pens.
Number of pens after Tammy gave away 24 staplers
= 5 x (1 u - 24)
= 5 u - 120
Number of pens in the end after Tammy bought another 192 pens
= 5 u - 120 + 192
= 5 u + 72
Number of markers and pens in the end is the same.
7 u = 5 u + 727 u - 5 u = 722 u = 72
1 u = 72 ÷ 2 = 36
Total numbers of staplers that Tammy had at first
= 1 u
= 36
Answer(s): 36
