[Math Lair] Linear Diophantine Equations Worksheet

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  1. Determine whether or not each of the following linear Diophantine equations has a solution and, if it does, find all its solutions.
    a. 14x − 35y + 77 = 0 b. −221x + 187y − 493 = 0
  2. A small clothing manufacturer produces two styles of sweaters, cardigan and pullover. He sells cardigans for $31 each and pullovers for $28 each. If his total revenue from a day's production is $1,460, how many of each type does he manufacture in a day?
  3. A man cashes a cheque for d dollars and c cents at a bank. The teller by mistake gives the man c dollars and d cents. The man doesn't notice the error until he has spent 23 cents, at which time he notices that he has 2d dollars and 2c cents. How much was the original cheque for?