Answer:
A. 12
Step-by-step explanation:
Let d represent the number of dimes and n represent the number of nickel.
We have been given that a collection of coins has 67 coins in all. This means that total number of nickels and dimes is 67. We can represent this information in an equation as:
[tex]n+d=67...(1)[/tex]
Since we know that a dime is worth $0.10, so d dimes will be worth 0.10d. A nickel is worth $0.05, so n nickels will be worth 0.05n.
We are also told that the collection is worth $6.10. We can represent this information in an equation as:
[tex]0.05n+0.10d=6.10...(2)[/tex]
We will use substitution method to solve system of linear equations.
From equation (1) we will get,
[tex]d=67-n[/tex]
Upon substituting [tex]d=67-n[/tex] in equation (2) we will get,
[tex]0.05n+0.10(67-n)=6.10[/tex]
[tex]0.05n+6.70-0.10n=6.10[/tex]
[tex]-0.05n+6.70=6.10[/tex]
[tex]-0.05n+6.70-6.70=6.10-6.70[/tex]
[tex]-0.05n=-0.60[/tex]
Let us divide both sides of our equation by [tex]-0.05[/tex].
[tex]\frac{-0.05n}{-0.05}=\frac{-0.60}{-0.05}[/tex]
[tex]n=12[/tex]
Therefore, there are 12 nickels in the collection and option A is the correct choice.
