Three types of horses are in a local...

Problema Solution

Three types of horses are in a local ranch. The number of Arabians is 8 more than twice the number of Quarter-horses, and the number of Clydesdales is 50 more than the number of Quarter horses.

There are a total of 282 horses at the ranch. How many of each kind are there?

Answer provided by our tutors

let

x = the number of Arabians

y = the number of Quarter-horses

z = the number of Clydesdales

the number of Arabians is 8 more than twice the number of Quarter-horses:

x = 8 + 2y

and the number of Clydesdales is 50 more than the number of Quarter horses:

z = 50 + y

there are a total of 282 horses at the ranch:

x +y + z = 282

by solving the system of equations:

x = 8 + 2y

z = 50 + y

x +y + z = 282

we find:

x = 120 Arabians

y = 56 Quarter-horses

z = 106 Clydesdales

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there are 120 Arabians, 56 Quarter-horses and 106 Clydesdales.

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