Your piggy bank has 25 coins in it; some are quarters and some are nickels. You have $3.45. How many nickels do you have?

First, let's call the number of quarters you have: #q#

And, the number of nickels you have: #n#

Using these variables and the information in the problem we can write two equations:

• Equation 1: #q + n = 25#

• Equation 2: #$0.25q + $0.05n = $3.45#

Step 1) Solve the first equation for #q#:

#q + n = 25#

#q + n - color(red)(n) = 25 - color(red)(n)#

#q + 0 = 25 - n#

#q = 25 - n#

Step 2) Substitute #(25 - n)# for #q# in the second equation and solve for #n# to find the number of nickels you have:

#$0.25q + $0.05n = $3.45# becomes:

#$0.25(25 - n) + $0.05n = $3.45#

#($0.25 xx 25) - ($0.25 xx n) + 0.05n = $3.45#

#$6.25 - $0.25n + 0.05n = $3.45#

#$6.25 + (-$0.25 + 0.05)n = $3.45#

#$6.25 + (-$0.20)n = $3.45#

#$6.25 - $0.20n = $3.45#

#$6.25 - color(red)($6.25) - $0.20n = $3.45 - color(red)($6.25)#

#0 - $0.20n = -$2.80#

#-$0.20n = -$2.80#

#(-$0.20n)/(color(red)(-)color(red)($)color(red)(0.20)) = (-$2.80)/(color(red)(-)color(red)($)color(red)(0.20))#

#(color(red)(cancel(color(black)(-$0.20)))n)/cancel(color(red)(-)color(red)($)color(red)(0.20)) = (color(red)(cancel(color(black)(-$)))2.80)/(cancel(color(red)(-)color(red)($))color(red)(0.20))#

#n = 2.80/color(red)(0.20)#

#n = 14#

You would have 14 nickels