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?

Please help me!!! :-)

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- Apr 30th 2012, 08:17 AMBuilderjay2011Geometry 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?

Please help me!!! :-) - Apr 30th 2012, 08:19 AMProve ItRe: Geometry Problem Using Linear Equation
The two numbers are consecutive, so we could call them $\displaystyle \displaystyle \begin{align*} x \end{align*}$ and $\displaystyle \displaystyle \begin{align*} x + 1 \end{align*}$.

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

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

Can you solve this equation for $\displaystyle \displaystyle \begin{align*} x \end{align*}$? Can you use this to determine what the two integers are? - Apr 30th 2012, 08:32 AMBuilderjay2011Re: 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. :(

- Apr 30th 2012, 08:39 AMProve ItRe: Geometry Problem Using Linear Equation
No, it says the first OF two consecutive integers is divided by 4, i.e. $\displaystyle \displaystyle \begin{align*} \frac{x}{4} \end{align*}$, and the second OF two consecutive integers is divided by 2, i.e. $\displaystyle \displaystyle \begin{align*} \frac{x + 1}{2} \end{align*}$.

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.) - Apr 30th 2012, 08:42 AMBuilderjay2011Re: Geometry Problem Using Linear Equation
Ohh, you're right it does say that. Let me work on solving it and see what you think. :)

- Apr 30th 2012, 10:19 AMBuilderjay2011Re: 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.

- Apr 30th 2012, 10:29 AMProve ItRe: Geometry Problem Using Linear Equation