- Determine whether or not each of the following linear Diophantine
equations has a solution and, if it does, find all its solutions.
a. 14 `x`− 35`y`+ 77 = 0b. −221 `x`+ 187`y`− 493 = 0 - 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?
- 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 2`d`dollars and 2`c`cents. How much was the original cheque for?