Folders cost $1.50 and binders cost $1.75. You want to spend exactly $14.00. The number of folders you bought was 3 more than twice the binders you bought.

Question

STEP 1) DEFINE YOUR VARIABLES

LET ____ = _______

LET ____ = _______

STEP 2) WRITE A SYSTEM OF EQUATIONS

EQUATION 1) _________

EQUATION 2) __________

Answer 1

Ya know, these confused me terribly when I first learned them.

First, we have to define our variables. In other words, we're gonna qssign a letter to each of what we're trying to find. There are some rules, but you can pretty much use any letters you want. I like to use the first letters, though I may have to change it up if I'm dealing with pens and pencils, for example.

Let f = the number of folders purchased.

Let b = the number of binders purchased.

If I buy 2 folders, I spend 1.5(2), right? If I buy 3 binders, I spend 1.75(3).

1.5f + 1.75b = 14

f = 2b + 3

I'm not going to explain, but hopefully you can see how I turned sentences into equations. Good luck!

Answer 2

For this problem we will let f = the # of folders and we will let b = the # of binders

So, we can now write the equation as 1.5f + 1.75 b = 14

But then they tell you that the number of folders you bought was 3 more than twice the number of binders, so that means that:

f = 2b + 3

So, your system of equations is:

1.5f + 1.75b = 14

f = 2b + 3

We can substitute (2b + 3) for "f" in the first equation, like this:

1.5(2b + 3) + 1.75b = 14

3b + 4.5 + 1.75b = 14

4.75b + 4.5 = 14

-4.5 -4.5

4.75b = 9.5

÷4.75 ÷4.75

b = 2

We can now plug that value in for b and then find the value of f and check our answers.

1.5f + 1.75b = 14

1.5f + 1.75(2) = 14

1.5f + 3.5 = 14

-3.5 -3.5

1.5f = 10.5

÷1.5 ÷1.5

f = 7

CHECK:

f = 2b + 3

7 = 2(2) + 3

7 = 4 + 3

7 = 7