80 coins (qrtrs, nickels); total value $14.60; find number

[van]

i'm having trouble with solving systems. i can use substitution or addition methods.
i have tried doing this one over and over and gone through an entire eraser just on this one alone:

Johnston and Betsy Waring have a jar containing 80 coins, all of which are either quarters or nickels. The total value of the coins is $14.60. How many of each type of coin to they have?

so, here's what I have tried:
let x = the number of quarters
let y = the number of nickels

x + y = 80
0.25x + 0.5y = 14.60

x = 80 - y
0.25(80-y) + 0.5y = 14.60
20 - 0.25y + 0.5 = 14.60
20.5 - 0.25y = 14.60
0.25y = -5.9
y = -23.6

so, i know that i messed up somewhere because they can't have a negative amount of nickels.
the answer should be x=53, y=27.
can anyone pint me in the right direction? thanks.

 

[arthur ohlsten]

Re: help with a word problem...

x=no. of quarters
y=no.of nickles

x+y=80
x[.25]+y[.05]=14.6
[80-y][.25]+.05y=14.60
20-.25y+.05y=14.6
20 - .20y=14.6

add .20y to each side
20=.20y +14.6

subtract 14.6 from each side
5.4=.2y
divide both sides by .2
y=27 answer
x=53 answer

Arthur

 

[van]

Re: help with a word problem...

oh good god... thanks alot.
i can't believe that i wrote .5 instead of .05

thanks arthur.

 

[arthur ohlsten]

Re: help with a word problem...

you are welcome.
It is a strange phenomina that we keep repeating the same error over and over when we check something. if your sum of a group of numbers is wrong, as you check it you keep making the same error over and over
Best of luck with your studies
Arthur