Question: A farmer goes to market and buys a hundred animals at a total cost of $1,000.00. The price of cows being $50.00 each, sheep $10.00 each, and rabbits 50¢ each, how many of each kind does he buy? Most people will solve this, if they succeed at all, by more or less laborious trial, but there are several direct ways of getting the solution.
Answer: The man bought 19 cows for $950.00, 1 sheep for $10.00, and 80 rabbits for $40.00, making together 100 animals at a cost of $1,000.00.
A purely arithmetical solution is not difficult by a method of averages, the average cost per animal being the same as the cost of a sheep.
By algebra we proceed as follows, working in dollars: Since x + y + z = 100
by subtraction, or 99x + 19y = 1900. We have therefore to solve this indeterminate equation. The only answer is x = 19, Y = l. Then, to make up the 100 animals, z must equal 80.
No comments:
Post a Comment