The ratio of saloon cars to the total number of cars on display in Ken's car shop was 2 : 5. ¹₃ of the remaining cars on display were electric cars and the rest were family cars and sports cars in the ratio of 5 : 2. If there were 56 more saloon cars than family cars, how many sports cars were there?

Saloon Cars	Electric Cars	Family Cars	Sports Cars	Total Cars
2x7	3x7			5x7
	1x7	2x7		3x7
		5x2	2x2
14 u	7 u	10 u	4 u

The total number of family cars and sports cars is the combined repeated identity. Make the total number of family cars and sports cars the same. LCM of 2 and 7 is 14.

The total number of electric cars, family cars and sports cars is the next combined repeated identity. Make the total number of electric cars, family cars and sports cars the same. LCM of 3 and 3 is 21. 

Number of more saloon cars than family cars
= 14 u - 10 u
= 4 u

4 u = 56

1 u = 56 ÷ 4 = 14

Number of sports cars
= 4 u
= 4 x 14
= 56

Answer(s): 56