Let x = number of armchairs
7 - x = number of stools
So, cost of x armchairs = 300x and
cost of 7 - x stools = 150(7 - x)
Then, 300x + 150(7 - x) = 1650
300x + 1050 - 150x = 1650
150x + 1050 = 1650
150x = 600
x = 4
Answer: there are 4 armchairs and 3 stools