The ratio of sports cars to the total number of cars on display in Ken's car shop was 3 : 8. ²₅ of the remaining cars on display were saloon cars and the rest were electric cars and family cars in the ratio of 9 : 2. If there were 90 more sports cars than electric cars, how many family cars were there?

Sports Cars	Saloon Cars	Electric Cars	Family Cars	Total Cars
3x11	5x11			8x11
	2x11	3x11		5x11
		9x3	2x3
33 u	22 u	27 u	6 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 3 and 11 is 33.

The total number of saloon cars, electric cars and family cars is the next combined repeated identity. Make the total number of saloon cars, electric cars and family cars the same. LCM of 5 and 5 is 55. 

Number of more sports cars than electric cars
= 33 u - 27 u
= 6 u

6 u = 90

1 u = 90 ÷ 6 = 15

Number of family cars
= 6 u
= 6 x 15
= 90

Answer(s): 90