A pen and a pencil together cost $5.10. The pen cost $5 more than the pencil. How much does each cost?

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