The ratio of saloon cars to the total number of cars on display in Ken's car shop was 4 : 11. ²₇ of the remaining cars on display were electric cars and the rest were sports cars and family cars in the ratio of 2 : 1. If there were 22 more saloon cars than sports cars, how many family cars were there?

Saloon Cars	Electric Cars	Sports Cars	Family Cars	Total Cars
4x3	7x3			11x3
	2x3	5x3		7x3
		2x5	1x5
12 u	6 u	10 u	5 u

The total number of sports cars and family cars is the combined repeated identity. Make the total number of sports cars and family cars the same. LCM of 5 and 3 is 15.

The total number of electric cars, sports cars and family cars is the next combined repeated identity. Make the total number of electric cars, sports cars and family cars the same. LCM of 7 and 7 is 21. 

Number of more saloon cars than sports cars
= 12 u - 10 u
= 2 u

2 u = 22

1 u = 22 ÷ 2 = 11

Number of family cars
= 5 u
= 5 x 11
= 55

Answer(s): 55