Can someone help me solve this word problem using a diophantine equation?
A man has $4.55 in change composed entirely of dimes and quarters. What are the maximum and minimum number of coins that he can have? Is it possible for the number of dimes to equal the number of quarters.
So far I set up what was given so I have: x= # of dimes y= # of quarters 455=total 10=cost of dime 25=cost of quarter
equation: 10x+25y=455 so I found the gcd(25,10)=5 and since gcd(25,10)|455 there is a solution.
where do I go from here?