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.) 


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