Question

Mike, a Salvation Army bell ringer, has 5 fewer quarters than nickels in his cup. If Mike has $5.95 in quarters and nickels, how many nickels does he have?

Answer 1

Let x=number of nickels in Mike's cup

Then x-5=number of quarters in Mike's cup  

Let's now deal in pennies to make life a little more simple.  

5x=amount of money that Mike has from the nickels  

25(x-5)=amount of money that Mike has from the quarters  

We are told that this adds up to 595. So our algebraic equation is:  

5x+25(x-5)=595 get rid of parens (Now as you well know, if we want to deal in dollars, we can just as easily write this equation as:

0.05x+0.25(x-5)=5.95), but lets continue to deal in pennies  

5x+25x-125=595 add 125 to both sides

5x+25x-125+125=595+125 collect like terms

30x=720 divide both sides by 30

x=24------------------------------------number of nickels  

x-5=24-5=19---------------------------------number of quarters  

CK

24(0.05)+19(0.25)=5.95

1.20+4.75=5.95

5.95=5.95