The ratio of sports 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 electric cars and the rest were saloon cars and family cars in the ratio of 3 : 2. If there were 294 more sports cars than saloon cars, how many family cars were there?

Sports Cars	Electric Cars	Saloon Cars	Family Cars	Total Cars
4x5	3x5			7x5
	1x5	2x5		3x5
		3x2	2x2
20 u	5 u	6 u	4 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 5 is 10.

The total number of electric cars, saloon cars and family cars is the next combined repeated identity. Make the total number of electric cars, saloon cars and family cars the same. LCM of 3 and 3 is 15. 

Number of more sports cars than saloon cars
= 20 u - 6 u
= 14 u

14 u = 294

1 u = 294 ÷ 14 = 21

Number of family cars
= 4 u
= 4 x 21
= 84

Answer(s): 84