math
posted by r. anthony .
Tashana has 16 coins that total to $1.85. She has only nickels, dimes and quarters. How many of each coin could
she have?

nickels  x
dimes  y
quarters  16xy
5x + 10y + 25(16xy) = 185
5x + 10y + 400  25x  25y = 185
20x  15y = 215
divide by 5
4x + 3y = 43
but x and y must be positive integers
we know the xintercept is < 11
and the yintercept < 14
y = (43  4x)/3
by inspection, if x = 4 , y = 9 is the only combination that will work
so she has 4 nickels, 9 dimes and 1649 or 3 quarters.
check:
does she have 16 coins ?
4+9+3 = 16 , yes
does she have $1.85 ?
4(5) + 9(10) + 25(3) = 185 , yes!! 
She could actualy do it several different combinations.
5 quarters, 1 dime, and 10 nickels
4 quarters, 5 dimes, and 7 nickels
3 quarters, 9 dimes, and 4 nickels
2 quarters, 13 dimes, and 1 nickel 
Should not have stopped after I found one.