Question 105150
"Your piggy bank has 25 coins in it; some are quarters and some are nickels."
First name your variables. 
Q-quarters
N-nickels
1.{{{Q+N=25}}}
Each quarter has a value of $0.25.
Each nickel has a value of $0.05.
"You have $3.45."
{{{0.25*Q+0.05*N=3.45}}}
2.{{{25Q+5N=345}}} Multiply both sides by 100 to get rid of the decimals. 
Use equation 1 and come up with an expression for Q and use it in 2. 
1.{{{Q+N=25}}}
{{{Q+N-N=25-N}}}
{{{Q=25-N}}}
Now substitute into 2. 
2.{{{25Q+5N=345}}}
{{{25(25-N)+5N=345}}}
{{{625-25N+5N=345}}}
{{{625-625-20N=345-625}}} Use the additive inverse of 625. 
{{{-20N=-280}}}
{{{-20N/(-20)=-280/(-20)}}} Use the multiplicative inverse of (-20). 
{{{N=14}}}
{{{Q=25-N}}}
{{{Q=25-14}}}
{{{Q=11}}} 
Check your answer
{{{25Q+5N=345}}}
{{{25(11)+5(14)=345}}}
{{{275+70=345}}}
{{{345=345}}}
Good answer. 
11 quarters and 14 nickels in the piggy bank.