There are two kinds of flowers in the flower shop: roses and carnations. A bunch of 9 roses, a bunch of 6 carnations. It is known that there are 50 fewer roses than carnations, and the total ratio of roses to carnations is 3: 7. How many roses are there in the flower shop?

Solution: If there are 3x roses and 7x carnations, then

3x 9+50 = 7x 6

x/3+50=7x/6

2x+300=7x

5x=300

x=60

3x= 180

7x=420

There are 180 roses and 420 carnations.