Question 424014: Marlisa has exactly $61 in one dollar, five dollar, and ten dollar bills. If she has 14 bills in all, how many of each bill does she have?
I know the answer is 3 ten-dollar bills, 5 five-dollar bills and 6 one-dollar bills, but is there a way to calculate without just doing trial and error
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! $1 bill x numbers
$5 bill y numbers
$10 bill z number
x+y+z=14................1
x+5y+10z=61............2
A Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations.
re write equation (1)
x= 14-y-z
substitute the value of x in (2)
14-y-z+5y+10z=61
4y+9z=47
z= 47/9 -4y/9
z=(47-4y)/9
Z should be a whole number.( it cannot be a fraction)
for what values y will z be a whole number
for y=5 ,
z=(47-4*5)/9
z=27/9
z=3
x=6, y =5, z=3
CHECK
6+25+30=61
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