In detail

The price of the horses

The price of the horses

150 years ago, the mathematician Morgan tried to demonstrate the practical nature of algebra with the following problem:

A person has two horses and a saddle. The chair is worth 50 pounds. If you place the chair on the first horse, its value is twice that of the second. But if you put it on the second, the value of the second horse is three times that of the first.

What is the price of each horse?

Solution

If we call x to the value of the first horse e Y to the value of the second horse we have to:

x + 50 = 2y
y + 50 = 3x

If we clear x in the first equation:
x = 2y - 50
y + 50 = 3 (2y - 50)
y + 50 = 6y - 150
y - 6y = -150 - 50
-5y = -200
5y = 200
y = 200/5 = 40
x = 2 · 40 - 50 = 80 - 50 = 30

Where do we deduce that the first horse costs 30 pounds and the second one costs 40 pounds.