Question

The Writing Emporium sells pencils and pens individually. Alana buys a pencil and two pens for $1.10. Jeffrey buys two pencils and a pen for $1.00. How much does Edward spend to buy six pencils and six pens from the Writing Emporium?

Answer 1

$4.20

Explanation:

The Writing Emporium sells pencils and pens individually.

Step 1

We have to first find the price of a pencil and a pen

Let:

The price of a pencil = x

The price of a pen = y

Alana buys a pencil and two pens for $1.10.

x + 2y = 1.1 ......Equation 1

x = 1.1 - 2y

Jeffrey buys two pencils and a pen for $1.00.

2x + y = 1 ........ Equation 2

We substitute 1.1 - 2y for x in Equation 2

2(1.1 - 2y) + y = 1

2.2 - 4y + y = 1

-4y + y = 1 - 2.2

-3y = -1.2

y = -1.2/-3

y = $0.4

Solving for x

x = 1.1 - 2y

x = 1.1 - 2(0.4)

x = 1.1 - 0.8

x = $0.3

Hence:

The price of a pencil = x = $0.3

The price of a pen = y = $0.4

Step 2

How much does Edward spend to buy six pencils and six pens from the Writing Emporium?

6x + 6y

6($0.3) + 6($0.4)

$1.8 + $2.4

= $4.20

Therefore, Edward spent $4.20 to buy six pencils and six pens from the Writing Emporium.