The ratio of saloon cars to the total number of cars on display in Ken's car shop was 2 : 7. ³₅ of the remaining cars on display were sports cars and the rest were electric cars and family cars in the ratio of 2 : 1. If there were 30 more saloon cars than electric cars, how many family cars were there?

Saloon Cars	Sports Cars	Electric Cars	Family Cars	Total Cars
2x3	5x3			7x3
	3x3	2x3		5x3
		2x2	1x2
6 u	9 u	4 u	2 u

The total number of electric cars and family cars is the combined repeated identity. Make the total number of electric cars and family cars the same. LCM of 2 and 3 is 6.

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

Number of more saloon cars than electric cars
= 6 u - 4 u
= 2 u

2 u = 30

1 u = 30 ÷ 2 = 15

Number of family cars
= 2 u
= 2 x 15
= 30

Answer(s): 30