Answer:
D
Step-by-step explanation:
Let n represent the number of nickels and d represent the number of dimes Chuin has.
Since Chuin has a total of 18 coins in his pocket, the sum of the number of nickels and dimes must total 18. So:
[tex]n+d=18[/tex]
The total worth of the coins is $1.45. Since each nickel is worth $0.05 and each dime is worth $0.10:
[tex]0.05n+0.1d=1.45[/tex]
Solve the system. We can use elimination (you can use substitution if you prefer, it works just as perfect!). First, multiply both sides of the second equation by 10:
[tex]0.5n+d=14.5[/tex]
Next, we can multiply the first equation by negative one:
[tex]-n-d=-18[/tex]
Add the two equations together:
[tex](0.5n+d)+(-n-d)=(14.5)+(-18)[/tex]
Simplify:
[tex]-0.5n=-3.5[/tex]
Divide both sides by -0.5. So:
[tex]n=7[/tex]
Chuin has seven nickels.
Using the first equation again, substitute n for 7 and solve for d:
[tex](7)+d=18\Rightarrow d=11[/tex]
Therefore, Chuin has seven nickels and 11 dimes.
Our answer is D.
