Question

Of the three different types of horses on a ranch, 1/4 are Arabians, 2/5 are Thoroughbreds, and the rest are Morgan's. What fraction of the horses are Morgan's?

Answer 1

The fraction of horses that are Morgan's=17/20

Explanation:

Step 1: Determine fraction for each breed

Arabians=1/4

Thoroughbreds=2/5

Morgan's=unknown

Step 2: Express each breed as a fraction of the total

Number of Arabians=fraction of Arabians×total number of horses

Let total number of horses be x

Arabians=(1/4)×x=1/4 x

Thoroughbreds=(2/5)×x=2/5 x

Morgans's=m

Step 3: Calculate fraction of Morgans

Total number of horses=Arabians+Thoroughbreds+Morgans

x=(1/4)x+(2/5)x+m

solve for m;

m=x-(1/4)x-(2/5)x

m=x-3/20x

m=17/20 x

The fraction of horses that are Morgan's=17/20