SOLUTION: The sum of three numbers is 120. The second number is 8 less than the first number, and the third is 4 more than the first number. This question is on a handout my child brought ho

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Question 214714: The sum of three numbers is 120. The second number is 8 less than the first number, and the third is 4 more than the first number. This question is on a handout my child brought home. There is no ISBN
Found 4 solutions by scott8148, Alan3354, drj, ptaylor:
Answer by scott8148(5891) About Me  (Show Source):
You can put this solution on YOUR website!
let n = "1st number"

"The second number is 8 less than the first number" ___ n - 8

"the third is 4 more than the first number" ___ n + 4

"The sum of three numbers is 120" ___ n + n - 8 + n + 4 = 120

3n - 4 = 120 ___ 3n = 124 ___ n = 124/3 = 41 1/3

substituting ___ n - 8 = 33 1/3

substituting ___ n + 4 = 45 1/3

Answer by Alan3354(21605) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of three numbers is 120. The second number is 8 less than the first number, and the third is 4 more than the first number.
-----------
n = 1st number
n-8 = 2nd
n+4 = 3rd
-----------
n + n-8 + n+4 = 120
3n - 4 = 120
3n = 124
n = 124/3
n = 41 1/3
2nd = 33 1/3
3rd = 45 1/3

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of three numbers is 120. The second number is 8 less than the first number, and the third is 4 more than the first number

Step 1. Let x be the first number

Step 2. Let x-8 be the second number since it's 8 less than the first number

Step 3. Let x+4 be the third number since it's 4 more than the first number

Step 4. Then, x+x-8+x+4=120 since we're given the sum of three numbers is 120.

Step 5. The following will solve the above equation in step 4.

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


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=41.3333333333333.
  • Graphical form: Equation x%2Bx-8%2Bx%2B4=120 was fully solved.
  • Text form: x+x-8+x+4=120 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x%2Bx-8%2Bx%2B4=120+%29
    For tutors: simplify_cartoon( x+x-8+x+4=120 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x%2Bx-highlight_red%28+8+%29%2Bx%2Bhighlight_red%28+4+%29=120.
Added fractions or integers together
It becomes x%2Bx%2Bhighlight_green%28+-4+%29%2Bx=120.
Look at x%2Bx%2Bhighlight_red%28+-4+%29%2Bx=120.
Moved -4 to the right of expression
It becomes x%2Bx%2Bx%2Bhighlight_green%28+-4+%29=120.
Look at x%2Bx%2Bx%2Bhighlight_red%28+-4+%29=120.
Removed extra sign in front of -4
It becomes x%2Bx%2Bx-highlight_green%28+4+%29=120.
Look at highlight_red%28+x+%29%2Bhighlight_red%28+x+%29%2Bhighlight_red%28+x+%29-4=120.
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+x+%29,highlight_red%28+x+%29 replacing them with highlight_green%28+%281%2B1%2B1%29%2Ax+%29
It becomes highlight_green%28+%281%2B1%2B1%29%2Ax+%29-4=120.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+1+%29%2Bhighlight_red%28+1+%29%29%2Ax-4=120.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2Ax-4=120.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2Ax+%29-4=120.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2Ax-4=120.
Look at 3%2Ax-4=highlight_red%28+120+%29.
Moved these terms to the left highlight_green%28+-120+%29
It becomes 3%2Ax-4-highlight_green%28+120+%29=0.
Look at 3%2Ax-highlight_red%28+4+%29-highlight_red%28+120+%29=0.
Added fractions or integers together
It becomes 3%2Ax%2Bhighlight_green%28+-124+%29=0.
Look at 3%2Ax%2Bhighlight_red%28+-124+%29=0.
Removed extra sign in front of -124
It becomes 3%2Ax-highlight_green%28+124+%29=0.
Look at highlight_red%28+3%2Ax-124+%29=0.
Solved linear equation highlight_red%28+3%2Ax-124=0+%29 equivalent to 3*x-124 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=41.3333333333333.

Universal Simplifier and Solver


Done!



With x=41.33333... or x=124%2F3

x-8=124%2F3-24%2F3=100%2F3

x%2B4=124%2F3%2B12%2F3=136%2F3

So the numbers are 124%2F3, 100%2F3, and 136%2F3 Note these numbers add up to 120.
I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J


Answer by ptaylor(1894) About Me  (Show Source):
You can put this solution on YOUR website!

OK
Let x=the first number
then x-8=second number
and x+4=third number
Now we are told that:
x+(x-8)+(x+4)=120 simplify
x+x-8+x+4=120
3x-4=120 add 4 to each side
3x-4+4=120+4 or
3x=124 divide each side by 3
x=41 1/3-----------first number
x-8=(41 1/3)-8=33 1/3------------second number
x+4=(41 1/3)+4=45 1/3 --------------------third number
CK
(41 1/3)+(33 1/3) + (45 1/3)=120
120=120
Hope this helps---ptaylor