There are 40 cars in a parking lot, all of which are 2-door or 4-door, and each car is either a compact car or an SUV. There are twice as many compact 4-door cars as compact 2-door cars, and three times as many 2-door SUVs as compact 2-door cars. If there are exactly as many compact 4-door cars as there are 4-door SUVs, then how many compact 2-door cars are in the parking lot?
x + 2x + 3x +2x = 40 and x =40 / 8 =5 compact 2-door cars in the parking lot.
40 Cars 2-door 4-door
Compact(C) 5 10
SUV(S) 15 10
--------- --------
Totals 20 20
+128475 2* compact 2-door = compact 4-door (1)
3* compact 2-door = SUV 2-door (2)
compact 4-door = SUV 4 door (3)
compact 2-door + SUV 2-door + compact 4-door + SUV 4-door = 40 (4)
Sub (1), (2) and (3) into (4)
Note that using (1) and (3).....2compact 2-door = SUV 4-door....so.....
compact 2-door + 3compact 2-door + 2*compact 2-door + 2*compact 2-door = 40
Simplifying....we have that
8 *compact 2-door =40 divide both sides by 8
compact 2-door = 40/8 = 5
Proof
There are 5 compact 2-door
There are 10 compact 4-door
There are 15 SUV 2-door
There are 10 SUV 4-door
