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 family cars and the rest were electric cars and sports cars in the ratio of 9 : 8. If there were 288 more saloon cars than electric cars, how many sports cars were there?

Saloon Cars	Family Cars	Electric Cars	Sports Cars	Total Cars
2x17	3x17			5x17
	1x17	2x17		3x17
		9x2	8x2
34 u	17 u	18 u	16 u

The total number of electric cars and sports cars is the combined repeated identity. Make the total number of electric cars and sports cars the same. LCM of 2 and 17 is 34.

The total number of family cars, electric cars and sports cars is the next combined repeated identity. Make the total number of family cars, electric cars and sports cars the same. LCM of 3 and 3 is 51. 

Number of more saloon cars than electric cars
= 34 u - 18 u
= 16 u

16 u = 288

1 u = 288 ÷ 16 = 18

Number of sports cars
= 16 u
= 16 x 18
= 288

Answer(s): 288