The ratio of family cars to the total number of cars on display in Ken's car shop was 2 : 7. ³₅ of the remaining cars on display were electric cars and the rest were saloon cars and sports cars in the ratio of 4 : 1. If there were 38 more family cars than saloon cars, how many sports cars were there?

Family Cars	Electric Cars	Saloon Cars	Sports Cars	Total Cars
2x5	5x5			7x5
	3x5	2x5		5x5
		4x2	1x2
10 u	15 u	8 u	2 u

The total number of saloon cars and sports cars is the combined repeated identity. Make the total number of saloon cars and sports cars the same. LCM of 2 and 5 is 10.

The total number of electric cars, saloon cars and sports cars is the next combined repeated identity. Make the total number of electric cars, saloon cars and sports cars the same. LCM of 5 and 5 is 25. 

Number of more family cars than saloon cars
= 10 u - 8 u
= 2 u

2 u = 38

1 u = 38 ÷ 2 = 19

Number of sports cars
= 2 u
= 2 x 19
= 38

Answer(s): 38