The ratio of saloon cars to the total number of cars on display in Ken's car shop was 2 : 7. ²₅ of the remaining cars on display were electric cars and the rest were sports cars and family cars in the ratio of 10 : 9. If there were 72 more saloon cars than sports cars, how many family cars were there?

Saloon Cars	Electric Cars	Sports Cars	Family Cars	Total Cars
2x19	5x19			7x19
	2x19	3x19		5x19
		10x3	9x3
38 u	38 u	30 u	27 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 3 and 19 is 57.

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 5 and 5 is 95. 

Number of more saloon cars than sports cars
= 38 u - 30 u
= 8 u

8 u = 72

1 u = 72 ÷ 8 = 9

Number of family cars
= 27 u
= 27 x 9
= 243

Answer(s): 243