Homework Help: math

Posted by r. anthony on Sunday, February 17, 2013 at 10:44pm.

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

math - Reiny, Monday, February 18, 2013 at 12:26am
nickels --- x
dimes --- y
quarters --- 16-x-y

5x + 10y + 25(16-x-y) = 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 x-intercept is < 11
and the y-intercept < 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 16-4-9 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!!
math - Jeff, Monday, February 18, 2013 at 12:33am
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
Jeff is right- math - Reiny, Monday, February 18, 2013 at 2:04am
Should not have stopped after I found one.

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