Answer:
There 138 quarters and 0 nickels.
The value of nickels is $0.
Step-by-step explanation:
A quarter is 0.25 of a dollar, and a nickel is 0.05 of a dollar. We are told that the total worth of nickels and dollars we have is 34.5, that is
[tex]0.25q+0.05n=34.5[/tex]
where [tex]q[/tex] is the number of quarters, and [tex]n[/tex] is the number of nickels.
We are also told that total number of coins is 138, that is
[tex]q+n=138[/tex]
so we have two equations:
[tex](1).\:0.25q+0.05n=34.5[/tex]
[tex](2).\:q+n=138[/tex]
To this system of equations we first solve for [tex]n[/tex] in second equation and substitute its value into the first equation:
[tex]n=138-q[/tex]
the first equation becomes
[tex]0.25q+0.05(138-q)=34.5[/tex]
[tex]0.2q+6.9=34.5[/tex]
[tex]\boxed{q=138}[/tex]
So we have 138 quarters.
Now we put this value into equation(2) and solve for [tex]n[/tex]
[tex]n+138=138[/tex]
[tex]\boxed{n=0}[/tex]
So we have 0 nickles and therefore their value is $0.
