Question

7.) A bag contains 112 coins consisting of nickels and dimes that areworth $7.85 How many nickels and how many dimes are in the bag?Use two variables to define the unknowns. SET UP a SYSTEM oflinear equations using the two variables. Solve the system toanswer the problem. SHOW ALL STEPS!!(10 pts)

Answer 1

let

number of nickels = x

number of dimes = y

Therefore,

x + y = 112

The total cost can be represented below

1 dime = 0.1 dollars

1 nickels = 0.05 dollars

Therefore,

0.05x + 0.1y = 7.85

x + 2y = 157

`\begin{gathered} x+y=112 \\ x+2y=157 \\ y=45 \\ \\ x+45=112 \\ x=112-45 \\ x=67 \end{gathered}`