SOLUTION: Juan has a jar containing eighty 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 does he have? Arbitra

Question 167378: Juan has a jar containing eighty 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 does he have?
Arbitrarily I tried 60 quarters, but that ended up $15.00; then I dropped it to 55 quarters, which ended up $13.75, but the remainng number of coins had to be 25 which would have brought the total to 80 coins (correct answer), but it equals $15.85 which is too much.(You see, I've been working at it.) Question: is there a formula for this stuff? Thank you very much.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Juan has a jar containing eighty 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 does he have?
:
Actually it is quite simple using two equations:
Let n = no. of nickels
let q = no. of quarters
;
Total coin equation
n + q = 80
or
n = (80-q)
:
Total value equation:
.05n + .25q = 14.60
:
From the 1st equation, substitute (80-q) for n
.05(80-q) + .25q = 14.60
4 - .05q + .25q = 14.60
-.05q + .25q = 14.60 - 4
.20q = 10.60
q =
q = 53 quarters
:
I'll let you find the no. of nickels
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