Tammy had some files, pencils and markers. The ratio of the number of files to the number of pencils was 7 : 1. After giving away 18 pencils, the ratio of the number of markers to the number of pencils was 3 : 1. Tammy bought another 158 markers. As a result, there were an equal number of files and markers. How many files did she have at first?
| |
Files |
Pencils |
Markers |
| Before |
7 u |
1 u |
|
| Change |
|
- 18 |
|
| After 1 |
|
1 u - 18 |
3 u - 54 |
| Change |
|
|
+ 158 |
| After 2 |
7 u |
1 u - 18 |
3 u + 104 |
Number of pencils after Tammy gave away 18 pencils
= 1 u - 18
After Tammy gave away 18 pencils, the ratio of the number of markers to the number of pencils became 3 : 1. This means that the number of pencils was 3 times as many as the number of markers.
Number of markers after Tammy gave away 18 pencils
= 3 x (1 u - 18)
= 3 u - 54
Number of markers in the end after Tammy bought another 158 markers
= 3 u - 54 + 158
= 3 u + 104
Number of files and markers in the end is the same.
7 u = 3 u + 1047 u - 3 u = 1044 u = 104
1 u = 104 ÷ 4 = 26
Total numbers of files that Tammy had at first
= 7 u
= 7 x 26
= 182
Answer(s): 182
