Math Help - Geometry Problem Using Linear Equation

1. Geometry Problem Using Linear Equation

If the first of two consectutive integers is divided by 4 and the second consecutive integer is divided by 2, the sum of quotients would be 5. What are the integers?

2. Re: Geometry Problem Using Linear Equation

Originally Posted by Builderjay2011
If the first of two consectutive integers is divided by 4 and the second consecutive integer is divided by 2, the sum of quotients would be 5. What are the integers?

The two numbers are consecutive, so we could call them \displaystyle \begin{align*} x \end{align*} and \displaystyle \begin{align*} x + 1 \end{align*}.

The first is being divided by 4, so we get \displaystyle \begin{align*} \frac{x}{4} \end{align*}, and the second is being divided by 2, so we get \displaystyle \begin{align*} \frac{x + 1}{2} \end{align*}.

We are told the sum of these quotients is 5, so \displaystyle \begin{align*} \frac{x}{4} + \frac{x + 1}{2} = 5 \end{align*}.

Can you solve this equation for \displaystyle \begin{align*} x \end{align*}? Can you use this to determine what the two integers are?

3. Re: Geometry Problem Using Linear Equation

It's just that the "wording" of the problem makes no sense. It mentions the first "two consecutive integers divided by 4", then it says the "second consecutive integer divided by 2". This makes no sense to me.

4. Re: Geometry Problem Using Linear Equation

Originally Posted by Builderjay2011
It's just that the "wording" of the problem makes no sense. It mentions the first "two consecutive integers divided by 4", then it says the "second consecutive integer divided by 2". This makes no sense to me.
No, it says the first OF two consecutive integers is divided by 4, i.e. \displaystyle \begin{align*} \frac{x}{4} \end{align*}, and the second OF two consecutive integers is divided by 2, i.e. \displaystyle \begin{align*} \frac{x + 1}{2} \end{align*}.

The wording makes perfect sense and my answer to your question was very clear. If you are unable to follow then you will need one-on-one tuition, which is more than can be provided on this site. (I am a private tutor though, if you live in Melbourne Australia I can help you.)

5. Re: Geometry Problem Using Linear Equation

Ohh, you're right it does say that. Let me work on solving it and see what you think.

6. Re: Geometry Problem Using Linear Equation

I got the result: 6 and 7. Hope that is right. At least it checks out right. 6/4 = 1.5 and 7/2 = 3.5, totaling 5.

7. Re: Geometry Problem Using Linear Equation

Originally Posted by Builderjay2011
I got the result: 6 and 7. Hope that is right. At least it checks out right. 6/4 = 1.5 and 7/2 = 3.5, totaling 5.
Yes, you're correct. Well done