Question

You spend $16 on 3 notebooks and x binders. Notebooks cost $2 each and binders cost $5 each. Write an equation you can use to find the number of binders you bought. Please explain what you did!

Answer 1

You multiply 3x2, which equals 6-16. You will get 10, and then you see that binders are $5. 5x2 equals ten, so you got 2 binders.

Answer 2

2 binders.

Explanation:

Let's define our problem.

Let
`n` identify our notebooks and
`b` our binders, where
`p` is the price and
`q` is the quantity.

We know that the sum of the quantity of each good multiplied by its price should not exceed $16 and this can be expressed by the following equation:

`p_(n) *q_(n)+p_(b)*q_(b)=16`

Now, which variables do we know?

We know that we bought 3 notebooks at $2 each, so:
`p_(n) =2 \\q_(n)=3`

On the other hand, we know that the binders cost $5 each, although we don't know how many we bought, so:
`p_(b) =5`

Substituting our known variables into our equation, we get:

`2 *3+5*q_(b)=16`

For which we solve:

`6+5*q_(b)=16`

Now you can use this equation to find the number of binders we bought, finding the value for the unknown variable.

`6+5*q_(b) =16\\5*q_(b) =16-6\\5*q_(b) =10\\q_(b)=(10)/(5) \\q_(b)=2`

So, according to our equation, we bought 2 binders at the price of $5 each.