The music center had 200 instruments. 70% of them were violins and the remaining are guitars. After a large sale of violins, the number of violins was 60% of all instruments. How many violins were sold?
The music center starts with 200 instruments, 70% were violins and the rest were guitars.
70% of 200 = 140 ---> so, it started with 140 violins and 60 guitars.
The center sold a bunch of violins and then the violins were only 60% of their instruments.
At this time 40% of its instruments were guitars.
This means that the 60 guitars represented 40% of their instruments.
To find how many instruments (call this total number "x") they still had, we can use this equation:
40% · x = 60 ---> 0.40x = 60 ---> x = 60 / 0.40 ---> 150
This means that the center still had 150 instruments,
So, they must have sold 200 - 150 = 50 instruments and, since they sold only violins,
they must have sold 50 violins..