Adding x+y will equal the total number of rooms (40). Multiplying (2 beds * the number of 2 bed rooms) and (3 beds * the number of 3 bed rooms), and adding those together, will equal the total number of beds (92).
x+y= 40 rooms 2x+3y= 92 beds
Solve for one variable in equation one and substitute it in equation two.
Solve for one variable: x+y= 40 Subtract y from both sides x= 40-y
Substitute (40-y) in for x in equation two: 2x+3y= 92 2(40-y) +3y= 92 80-2y+3y=92 Subtract 80 from both sides y= 12 three bed rooms
Substitute 12 in for y in either equation: x+y= 40 x+12= 40 x= 28 two bed rooms