The ratio of electric cars to the total number of cars on display in Ken's car shop was 4 : 7. ¹₃ of the remaining cars on display were sports cars and the rest were saloon cars and family cars in the ratio of 9 : 8. If there were 550 more electric cars than saloon cars, how many family cars were there?

Electric Cars	Sports Cars	Saloon Cars	Family Cars	Total Cars
4x17	3x17			7x17
	1x17	2x17		3x17
		9x2	8x2
68 u	17 u	18 u	16 u

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

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

Number of more electric cars than saloon cars
= 68 u - 18 u
= 50 u

50 u = 550

1 u = 550 ÷ 50 = 11

Number of family cars
= 16 u
= 16 x 11
= 176

Answer(s): 176