Answer:
The pen costs $5.05, and the pencil costs $0.05
Step-by-step explanation:
First, we define 2 variables for the two prices.
Let x = price of the pen.
Let y = price of the pencil.
Now we use the given information to write two equations.
"A pen and a pencil together cost $5.10. "
x + y = 5.1
"The pen cost $5 more than the pencil. "
y = x + 5
The system of equations is:
x + y = 5.1
y = x + 5
Since the second equation is already solved for y, we will use the substitution method to solve the system of equations.
Substitute y of the first equation by x + 5.
x + x + 5 = 5.1
2x + 5 = 5.1
2x = 0.1
x = 0.05 (price of the pencil)
Now substitute 0.05 for x in the second equation.
y = 0.05 + 5
y = 5.05 (price of the pen)
The pen costs $5.05, and the pencil costs $0.05
