# Need help determining proper equation. Please!

#### dawgs-mouse4

##### New member
I am told to use an equation to model and solve this problem:

A company buys a copier for $10,000. The IRS values the copier at$10,000(1 - n/20) after n years. After how many years will the copier be valued at $6500? I know that the answer is 7 years since I can see that n/20 = 5% per year, which is$500 per year in this case, but I don't know how to write the equation to model this. I'd really appreciate any help you can give me. Thanks! :?

#### mmm4444bot

##### Super Moderator
Staff member
dawgs-mouse4 said:
I can see that n/20 = 5% per year

This statement is not properly worded.

I think you mean "per year for n years".

1/20 = 5% is deducted per year, not n/20.

I don't know how to write the equation

Maybe you're overthinking it.

They want to know what value of n causes the expression 10000(1-n/20) to evaluate to 6500.

Therefore, the equation is simply:

10000(1 - n/20) = 6500

This is a linear equation; it can be put into Slope-Intercept form:

v = -500n + 10000

where v represents the irs-value of the copier after n years

To find the number of years that it takes the copier to reach a specific irs-value, substitute that value for v and solve for n.

6500 = -500n + 10000

The graph of v (the red line below) shows that the copier's irs-value depreciates to \$0 after 20 years.

[attachment=0:5ysfl283]irs.JPG[/attachment:5ysfl283]

#### dawgs-mouse4

##### New member
Thank you for your help! Is there another way to solve this? While you have taught me something new, and I understand what you have shown me, I am not to Slope-Intercept form yet in math. This is part of a chapter on distributive property and combining like terms. How would I create and solve the equation with these limitations? Using the equation 10,000(1-n/20)=6500, I am unsure how to use the distributive property to multiply 10,000 by a fraction. We haven't covered this yet, but it is part of my homework.

Thank you so much for any more help you can give me!

#### mmm4444bot

##### Super Moderator
Staff member

I assumed too much (since you asked about nothing specific, other than requesting the equation) by thinking that you already knew how to solve linear equations algebraically.

So, if I've got it straight now, you already know how to apply the Distributive Property, but you're not sure how to multiply the factors 10000 and n/20.

We multiply algebraic fractions the same way as when doing arithmetic with Rational numbers: numerator times numerator OVER denominator times denominator.

$$\displaystyle \frac{10000}{1} \cdot \frac{n}{20} = \frac{10000 \cdot n}{1 \cdot 20} = \frac{10000n}{20}$$

We reduce the Rational number 10000/20 to 500/1, and we write just 500.

I mean, 10000n/20 is 500n.

Distributive Property:

10000(1 - n/20)

10000(1) - 10000(n/20)

10000 - 500n

The equation is:

6500 = 10000 - 500n

In algebra, there are often different ways to solve equations. For example, you could perform either one of the following.

(1) Add 500n to both sides, and subtract 6500 from both sides

OR

(2) Subtract 10000 from both sides

If we do the steps in (1), we get:

500n = 3500

Divide both sides by 500, reduce the Rational number, and you're done.

If we do the steps in (2), we get:

-3500 = -500n

Divide both sides by -500, reduce the Rational number, and you're done.

Two different ways; same result.