Question

The sum of two books and a pencil is $6.00. The difference of cost between 3 books and 2 pencils is $ 2.00. Find the cost of a book and a pencil.​

Answer 1

Answer:

The book costs $2 and the pencil also costs $2.

Step-by-step explanation:

It is easy to get the value of the book and the pencil if we use algebraic expressions.

Let x be the cost of the book and let y be the cost of the pencil.

The sum of 2 books and a pencil is $6.00

• 2x + y = $6.00

The difference of cost between 3 books and 2 pencils is $2.00.

• 3x - 2y = $2.00

Step 1: Let's get the value of y first.

2x + y = 6

y = 6 - 2x

Step 2: Let's substitute the value of y and look for the value of x.

3x - 2y = $2.00

3x - 2(6-2x) = 2

3x - 12 + 4x = 2

7x = 12 + 2

7x = 14

x = $\frac{14}{7}$

x = $2 (this is the cost of the book)

Step 3: Let's substitute the value of x and look for the value of y.

2x + y = 6

2 (2) + y = 6

4 + y = 6

y = 6 - 4

y = $2 (this is the cost of the pencil)

Let's check:

2x + y = $6

2(2) + 2 = 6

4 + 2 = 6

6 = 6 (CORRECT)