Can you please help me

Question

A book and a pen cost $18. The book and 2 pens cost $21. What is the cost of the book?

Answer 1

This is a systems of equations problem. We must recognize that there are two different scenarios listed in the problem to start.

Part 1: A book and a pen cost $18. We must represent the cost of a book and pen with different variables, x and y, to distinguish between them. Let's set x = cost of books and y = cost of pens. The words "a book" and "a pen" mean one of each. So we have 1 book + 1 pen costs $18. In algebra, this can be written as x + y = 18.

Part 2: The book and 2 pens cost $21. Using x and y, we get 1 book and 2 pens costs $21, or x + 2y = 21

System:

x + y = 18

x + 2y = 21

Let's subtract the bottom equation from the top to ELIMINATE X.

x + y = 18

-(x + 2y = 21) <--- x - x = 0 ; y - 2y = -y ; 18 - 21 = -3

-y = -3 <--- divide both sides by -1 to isolate y.

y = 3

Plug y = 3 into first equation:

x + 3 = 18

x = 15

We have x=15 and y=3, meaning a book costs $15 and a pen costs $3.

Answer 2

If:

A book and a pen cost $18,

The book and 2 pens cost $21

The pen must cost $3 because we are adding $3 to the total when we add one pen,

Therefore one book costs $15 because it is $3 less than $18 when we include one pen.