Given:
In a jar, there are 5 fewer quarters than nickels.
The total value of the coins is $4.45.
To find:
The system of equations can be used to determine the number of quarters, q, and the number of nickels, n.
Solution:
Let q be the number of quarters and n be the number of nickels.
It is given that there are 5 fewer quarters than nickels.
[tex]q=n-5[/tex] ...(i)
We know that,
1 quarter = $0.25
1 nickel = $0.05
Using these conversions, we get
q quarters = $0.25q
n nickels = $0.05n
The total value of the coins is $4.45.
[tex]0.25q+0.05n=4.45[/tex] ...(ii)
The equations (i) and (ii) are equations of required system of equations.
Therefore, the system of equations is:
[tex]q=n-5[/tex]
[tex]0.25q+0.05n=4.45[/tex]
