The ratio of saloon 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 electric cars and the rest were sports cars and family cars in the ratio of 7 : 6. If there were 126 more saloon cars than sports cars, how many family cars were there?

Saloon Cars	Electric Cars	Sports Cars	Family Cars	Total Cars
3x13	5x13			8x13
	2x13	3x13		5x13
		7x3	6x3
39 u	26 u	21 u	18 u

The total number of sports cars and family cars is the combined repeated identity. Make the total number of sports cars and family cars the same. LCM of 3 and 13 is 39.

The total number of electric cars, sports cars and family cars is the next combined repeated identity. Make the total number of electric cars, sports cars and family cars the same. LCM of 5 and 5 is 65. 

Number of more saloon cars than sports cars
= 39 u - 21 u
= 18 u

18 u = 126

1 u = 126 ÷ 18 = 7

Number of family cars
= 18 u
= 18 x 7
= 126

Answer(s): 126