Recreational Mathematics

Algebraic Puzzles

Many puzzles are easily solved with an algebraic approach.

(1) A worker will be paid $10000 and a computer for a year's work. But he left after 7 months and got the computer and $2000 instead. How much is the computer worth?

(2) Find 3 numbers such that the first with half the other two, the second with 1/3 the other two, and the third with 1/4 the other two, shall each be equal to 34

Next Page: The Mathematician Test.

Answers:

(1) Let computer worth x, then 2000 + x = 7/12 (10000 + x), solving gives x = $9200.

(2) Let the numbers be x, y, z, then ¹/₂(x+y)+z = 34 Þ z = 34-¹/₂(x+y). This leaves 2 possibilities (a) 1/3(x+z)+y = 1/4(y+z)+x = 34 or (b) 1/4(x+z)+y = 1/3(y+z)+x = 34 solving and eliminating one of these 2 possibilities gives 10, 22, 26.