How to Solve a System of Equations with Pen and Notebook Costs

What is the cost of 1 pen and 1 notebook?

A. $5
B. $6
C. $7
D. $8

Answer:

The cost of 1 pen and 1 notebook is $5. Option A.

To find the cost of 1 pen and 1 notebook, we can solve the system of equations provided. Let x represent the cost of a pen and y represent the cost of a notebook. From the given equations, we have: 3x + 2y = 12 (equation 1) x + 3y = 11 (equation 2) We can use the elimination method to solve this system of equations. By multiplying equation 2 by 2, we get: 2x + 6y = 22 Now, subtract this new equation from equation 1: (3x + 2y) - (2x + 6y) = 12 - 22 x - 4y = -10 x = 4y - 10 Substitute x = 4y - 10 into equation 2: 4y - 10 + 3y = 11 7y = 21 y = 3 Now, substitute y = 3 back into x = 4y - 10: x = 4(3) - 10 x = 12 - 10 x = 2 Therefore, the cost of 1 pen is $2 and the cost of 1 notebook is $3. The total cost of 1 pen and 1 notebook is $2 + $3 = $5.