Abi had some markers, pens and pencils. The ratio of the number of markers to the number of pens was 6 : 1. After giving away 20 pens, the ratio of the number of pencils to the number of pens was 4 : 1. Abi bought another 174 pencils. As a result, there were an equal number of markers and pencils. How many markers did she have at first?
| |
Markers |
Pens |
Pencils |
| Before |
6 u |
1 u |
|
| Change |
|
- 20 |
|
| After 1 |
|
1 u - 20 |
4 u - 80 |
| Change |
|
|
+ 174 |
| After 2 |
6 u |
1 u - 20 |
4 u + 94 |
Number of pens after Abi gave away 20 pens
= 1 u - 20
After Abi gave away 20 pens, the ratio of the number of pencils to the number of pens became 4 : 1. This means that the number of pens was 4 times as many as the number of pencils.
Number of pencils after Abi gave away 20 pens
= 4 x (1 u - 20)
= 4 u - 80
Number of pencils in the end after Abi bought another 174 pencils
= 4 u - 80 + 174
= 4 u + 94
Number of markers and pencils in the end is the same.
6 u = 4 u + 946 u - 4 u = 942 u = 94
1 u = 94 ÷ 2 = 47
Total numbers of markers that Abi had at first
= 6 u
= 6 x 47
= 282
Answer(s): 282
