Answer:
D
Step-by-step explanation:
Let <em>n</em> represent the number of nickels and <em>d</em> 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:
![n+d=18](https://tex.z-dn.net/?f=n%2Bd%3D18)
The total worth of the coins is $1.45. Since each nickel is worth $0.05 and each dime is worth $0.10:
![0.05n+0.1d=1.45](https://tex.z-dn.net/?f=0.05n%2B0.1d%3D1.45)
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:
![0.5n+d=14.5](https://tex.z-dn.net/?f=0.5n%2Bd%3D14.5)
Next, we can multiply the first equation by negative one:
![-n-d=-18](https://tex.z-dn.net/?f=-n-d%3D-18)
Add the two equations together:
![(0.5n+d)+(-n-d)=(14.5)+(-18)](https://tex.z-dn.net/?f=%280.5n%2Bd%29%2B%28-n-d%29%3D%2814.5%29%2B%28-18%29)
Simplify:
![-0.5n=-3.5](https://tex.z-dn.net/?f=-0.5n%3D-3.5)
Divide both sides by -0.5. So:
![n=7](https://tex.z-dn.net/?f=n%3D7)
Chuin has seven nickels.
Using the first equation again, substitute <em>n</em> for 7 and solve for <em>d: </em>
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Therefore, Chuin has seven nickels and 11 dimes.
Our answer is D.