Question

The ratio of the number of red pens to the number of black pens in a
bookstore was 3: 7. An equal number of red pens and black pens were
sold. In the end, the ratio of the number of red pens left to the number
of black pens left was 5: 13.
There were 20 red pens in the end.
How
many red pens were sold?

Answer 1

started with 3 k red and 7 k black, total 10 k
s of each sold
so
red left = 3 k - s = 20 so s = 3 k - 20
black left = 7 k - s
total left = 10 k - 2 s
5/13 = red left / black left = (3k-s) / (7k-s)
5/13 = (3 k - 3k+20) / (7k -3k+20)
5/13 = 20 / (4k + 20)
260 = 20 k + 100
20 k = 160
k = 80
so s = 3k-20 = 240-0 = 220