SOLUTION: Your piggy bank has 25 coins in it; some are quarters and some are nickels. You have $3.45. How many quarters and nickels do you have? (I know you can figure this out by trial and

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Question 66569: Your piggy bank has 25 coins in it; some are quarters and some are nickels. You have $3.45. How many quarters and nickels do you have? (I know you can figure this out by trial and error, but you must write the equations and solve.)
Hint: You have two unknowns: "q" for quarters and "n" for nickels. You need two equations. Write one equation for the number of coins that you have and a second equation for the value of the coins. (An unknown number of nickels would have the value of .05n.)

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Your piggy bank has 25 coins in it; some are quarters and some are nickels. You have $3.45. How many quarters and nickels do you have? (I know you can figure this out by trial and error, but you must write the equations and solve.)
Hint: You have two unknowns: "q" for quarters and "n" for nickels. You need two equations. Write one equation for the number of coins that you have and a second equation for the value of the coins. (An unknown number of nickels would have the value of .05n.)

Let q= number of quarters
Then n=number of nickels
Equation (1) q+n=25
Value of the quarters (.25q) plus the value of the nickels (.05n) equals $3.45
Equation (2) .25q+.05n=$3.45
So we need to solve:
(1) q+n=25
(2) .25q+.05n=3.45

Multiply (1) by .05
(1a) .05q+.05n=1.25
(2a) .25q+.05n=3.45
subtract(1) from (2)
.20q=2.20
q=11 quarters
substitute in (1) above:
11+n=25 subtract 11 from both sides
n=14 nickels
Ck
11+14=25
and
11(.25)+14(.05)=3.45
2.75+.70=3.45
3.45=3.45
Actually, we can solve this problem with one unknown:
Let x=number of quartsrs
Then 25-x=number of nickels
(Now lets deal in pennies)
25x+5(25-x)=345
25x+125-5x=345 subtract 125 from both sides
20x=220
x=11 quarters
25-x=25-11=14 nickels

Hope this helps -----ptaylor