A sporting goods store sells right-handed baseball gloves and left handed baseball gloves. In 1 month 12 gloves were sold for a total revenue of $561. Right-handed gloves cost $45 and left-handed gloves cost $52. How many of each type of gloves did they sell?

x = number of right-handed gloves
12 - x = number of left-handed gloves

45x + 52 (12 - x) = 561
distribute
45x + 624 - 52x = 561
combine like terms
-7x + 624 = 561
subtract 624 from both sides
-7x = -63
divide both sides by -7
x = 9 (amount of right handed gloves)

12 - 9 = 3 (amount of left handed gloves)