Author Topic: 8th Grade Advance Math: Consecutive Number Algebraic Equations  (Read 419 times)

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Offline Hjowowsbdbdsuisjcbd

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8th Grade Advance Math: Consecutive Number Algebraic Equations
« on: October 07, 2014, 07:35:13 pm »
So, I was very sick recently and out of school for 4 days. I am trying to do these math problems but I simply do not get how to write an equation for the question. The question is in a word problem format and gives me a single number with several different integers. I would also like to point out that math is my worst subject so don't judge. :) I have till Friday to turn all my make-up work in so I am open to suggestions till then.

Here is one of the questions...

The sum of two consecutive even integers is 22 less than four times the smaller of the two numbers. Fine the larger of the two integers.

And another example...

The sum of 3 consecutive even integers is 30 more than the smallest integer. Find the largest integer.
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Offline Koala123

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Re: 8th Grade Advance Math: Consecutive Number Algebraic Equations
« Reply #1 on: October 07, 2014, 07:44:18 pm »
Question 1:  The sum of twoconsecutive even integers is 22 less than 4 times the smaller of the two numbers. Find the larger of the two integers.
Lets first make a variable, x, which equals the small number.  Consecutive integers means two numbers that follow up one another.  In this example, it is 10/12, or 12/14, etc.
So, in order to make this an equation, it is (x)+(x+2), because the second number will be 2 larger than the first.  The sum of that is 22 less than four times x, or the smaller integer.  So, the equation set up is
X+x+2=4x-22
You then just solve that.
2x+2=4x-22
24=2x
x=12
So, the smaller number of the two is 12, which makes the larger integer 14.

I'll also do number 2 for you.
The sum of 3 consecutive even integers is 30 more than thesmallest integer.  Find the largest integer.
We will again use x as the smallest integer.
x+(x+2)+(x+4)
This shows the consecutive even integers.  And since this is 30 more than the smallest integer, we can turn that into an equation.
x+x+2+x+4-30=x
Then you simplify
3x-24=x
2x=24
x=12
The largest integer is 12+4, or 16.
Hoped it helped!
                   

Offline Hjowowsbdbdsuisjcbd

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Re: 8th Grade Advance Math: Consecutive Number Algebraic Equations
« Reply #2 on: October 07, 2014, 08:24:30 pm »
Thank you so much, I think I got the hang of it now.
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Offline Koala123

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Re: 8th Grade Advance Math: Consecutive Number Algebraic Equations
« Reply #3 on: October 07, 2014, 08:26:42 pm »
No Problem!