SOLUTION: Hi, I don't know how to do consecutive odd/even integers. Such as this problem: Find three consecutive integers whose sum is 36. I know it's x+(x+2)+(x+3). Am I rig

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Question 223562: Hi, I don't know how to do consecutive odd/even integers.
Such as this problem:

Find three consecutive integers whose sum is 36.

I know it's x+(x+2)+(x+3). Am I right? After all, they are 'consecutive', they are not odd or even.

Then the other one is:

Find two consecutive even integers whose sum is 126.


I did the first one, x+x+2=126
Then I subtracted two from both sides, and got x+x=124. Then I added like terms and got 2x=124. And then I simply divided by 2. And got 62.
I did the last question from another guy who answered another guy. But he didn't explain HOW to get the other one. I know the other answer is 64...but I do not know how to get it!
Please explain it clearly as I have an Algebra Test tomorrow, and I want to ace it.

Thanks. :)

Found 2 solutions by brich, drj:
Answer by brich(7) About Me  (Show Source):
You can put this solution on YOUR website!
First Question:
your logic was correct but your equation was slightly off.
I think you meant to say:
x+(x+1)+(x+2)=36
Second Question:
you were right about this and the second number is very easy to get:
If you let the first number = x
and the next even integer = x+2
then x+(x+2)=126 like you stated above
you found x to = 62 so plug it in for x:
62+(62+2)=126
remember the entire sum inside the parentheses is equal to the next even number
do you see the answer you were looking for yet?
subtract 62 from both sides if you aren't sure
and the right side of the equation should now = 64
this means that 64 must be the second number, and that would make sense because its the next even number.
hope that helped.
let me know :)

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find three consecutive integers whose sum is 36.

Step 1. Let n be the first integer.

Step 2. Let n+1 and n+2 be the next two consecutive integers.

Step 3. Then n+n+1+n+2=36 since the sum is 36.

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: n=11.
  • Graphical form: Equation n%2Bn%2B1%2Bn%2B2=36 was fully solved.
  • Text form: n+n+1+n+2=36 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+n%2Bn%2B1%2Bn%2B2=36+%29
    For tutors: simplify_cartoon( n+n+1+n+2=36 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at n%2Bn%2Bhighlight_red%28+1+%29%2Bn%2Bhighlight_red%28+2+%29=36.
Added fractions or integers together
It becomes n%2Bn%2Bhighlight_green%28+3+%29%2Bn=36.
Look at n%2Bn%2Bhighlight_red%28+3+%29%2Bn=36.
Moved 3 to the right of expression
It becomes n%2Bn%2Bn%2Bhighlight_green%28+3+%29=36.
Look at highlight_red%28+n+%29%2Bhighlight_red%28+n+%29%2Bhighlight_red%28+n+%29%2B3=36.
Eliminated similar terms highlight_red%28+n+%29,highlight_red%28+n+%29,highlight_red%28+n+%29 replacing them with highlight_green%28+%281%2B1%2B1%29%2An+%29
It becomes highlight_green%28+%281%2B1%2B1%29%2An+%29%2B3=36.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+1+%29%2Bhighlight_red%28+1+%29%29%2An%2B3=36.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2An%2B3=36.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2An+%29%2B3=36.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2An%2B3=36.
Look at 3%2An%2B3=highlight_red%28+36+%29.
Moved these terms to the left highlight_green%28+-36+%29
It becomes 3%2An%2B3-highlight_green%28+36+%29=0.
Look at 3%2An%2Bhighlight_red%28+3+%29-highlight_red%28+36+%29=0.
Added fractions or integers together
It becomes 3%2An%2Bhighlight_green%28+-33+%29=0.
Look at 3%2An%2Bhighlight_red%28+-33+%29=0.
Removed extra sign in front of -33
It becomes 3%2An-highlight_green%28+33+%29=0.
Look at highlight_red%28+3%2An-33+%29=0.
Solved linear equation highlight_red%28+3%2An-33=0+%29 equivalent to 3*n-33 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=11.

Universal Simplifier and Solver


Done!



So n=11, n%2B1=12 and n%2B2=13 Note integers add up to 36

Step 4. ANSWER: The integers are 11, 12, and 13.


Find two consecutive even integers whose sum is 126.

Step 1. Let n be the first even integer

Step 2. Let n+2 be the next consecutive even integers

Step 3. Then, n+n+2=126 since the sum is 126.

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: n=62.
  • Graphical form: Equation n%2Bn%2B2=126 was fully solved.
  • Text form: n+n+2=126 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+n%2Bn%2B2=126+%29
    For tutors: simplify_cartoon( n+n+2=126 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+n+%29%2Bhighlight_red%28+n+%29%2B2=126.
Eliminated similar terms highlight_red%28+n+%29,highlight_red%28+n+%29 replacing them with highlight_green%28+%281%2B1%29%2An+%29
It becomes highlight_green%28+%281%2B1%29%2An+%29%2B2=126.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+1+%29%29%2An%2B2=126.
Added fractions or integers together
It becomes %28highlight_green%28+2+%29%29%2An%2B2=126.
Look at highlight_red%28+%28highlight_red%28+2+%29%29%2An+%29%2B2=126.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes highlight_green%28+2+%29%2An%2B2=126.
Look at 2%2An%2B2=highlight_red%28+126+%29.
Moved these terms to the left highlight_green%28+-126+%29
It becomes 2%2An%2B2-highlight_green%28+126+%29=0.
Look at 2%2An%2Bhighlight_red%28+2+%29-highlight_red%28+126+%29=0.
Added fractions or integers together
It becomes 2%2An%2Bhighlight_green%28+-124+%29=0.
Look at 2%2An%2Bhighlight_red%28+-124+%29=0.
Removed extra sign in front of -124
It becomes 2%2An-highlight_green%28+124+%29=0.
Look at highlight_red%28+2%2An-124+%29=0.
Solved linear equation highlight_red%28+2%2An-124=0+%29 equivalent to 2*n-124 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=62.

Universal Simplifier and Solver


Done!



n=62 and n%2B2=64

Step 4. ANSWER: The consecutive even integers are 62 and 64

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J