Tammy had some pens, markers and pencils. The ratio of the number of pens to the number of markers was 6 : 1. After giving away 25 markers, the ratio of the number of pencils to the number of markers was 3 : 1. Tammy bought another 198 pencils. As a result, there were an equal number of pens and pencils. How many pens did she have at first?
| |
Pens |
Markers |
Pencils |
| Before |
6 u |
1 u |
|
| Change |
|
- 25 |
|
| After 1 |
|
1 u - 25 |
3 u - 75 |
| Change |
|
|
+ 198 |
| After 2 |
6 u |
1 u - 25 |
3 u + 123 |
Number of markers after Tammy gave away 25 markers
= 1 u - 25
After Tammy gave away 25 markers, the ratio of the number of pencils to the number of markers became 3 : 1. This means that the number of markers was 3 times as many as the number of pencils.
Number of pencils after Tammy gave away 25 markers
= 3 x (1 u - 25)
= 3 u - 75
Number of pencils in the end after Tammy bought another 198 pencils
= 3 u - 75 + 198
= 3 u + 123
Number of pens and pencils in the end is the same.
6 u = 3 u + 1236 u - 3 u = 1233 u = 123
1 u = 123 ÷ 3 = 41
Total numbers of pens that Tammy had at first
= 6 u
= 6 x 41
= 246
Answer(s): 246
