Question

Sally bought six pencils and three folders for $3.90. Henry bought two pencils and five folders for $3.30. Which system of equations can be used to find the price in dollars of each pencil, x, and each folder, y.

Answer 1

The pencils cost $0.4 each and the folders $0.5.

Explanation:

Since Sally bought six pencils and three folders for $3.9. We have the following expression:

6*penchils + 3*folders = 3.9

And since Henry bought two pencils and five folders for $3.3. We have the following expression:

2*pencils + 5*folders = 3.3

The system of equations is given by:

6*pencils + 3*folders = 3.9

2*pencils + 5*folders = 3.3

In order to solve it we will multiply the second equation by -3 and sum both equations:

6*pencils + 3*folders = 3.9

-6*pencils - 15*folders = -9.9

We have:

-12*folders = -6

folders = 0.5

2*pencils + 5*0.5 = 3.3

2*pencils + 2.5 = 3.3

2*pencils = 3.3 - 2.5

2*pencils = 0.8

pencils = 0.8/2 = 0.4

The pencils cost $0.4 each and the folders $0.5.