SOLUTION: The sum of thre numbers is 40. One number is 5 more than the second number. It is twice the third number. What are the numbers.

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Question 215309: The sum of thre numbers is 40. One number is 5 more than the second number. It is twice the third number. What are the numbers.
Found 3 solutions by ankor@dixie-net.com, drj, MathTherapy:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of three numbers is 40.
x + y + z = 40
:
One number is 5 more than the second number.
x = y + 5
or
y = x - 5
:
It is twice the third number.
x = 2z
or
z = .5x
:
What are the numbers.
:
Substitute for y & z
x + (x-5) + .5x = 40
x + x + .5x = 40 + 5
2.5x = 45
x = 45%2F2.5
x = 18
then
y = 18-5
y = 13
and
z = .5(18)
z = 9
:
Check: 18 + 13 + 9 = 40

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of three numbers is 40. One number is 5 more than the second number. It is twice the third number. What are the numbers.

Step 1. Let x be one number, 5+x be the second number, and x/2 is the third number (since the number is twice the third number)

Step 2. The the sum is x+5+x+x/2=40 or

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


YOUR ANSWER


  • This is an equation! Solutions: x=14.
  • Graphical form: Equation x%2B5%2Bx%2Bx%2F2=40 was fully solved.
  • Text form: x+5+x+x/2=40 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x%2B5%2Bx%2Bx%2F2=40+%29
    For tutors: simplify_cartoon( x+5+x+x/2=40 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x%2Bhighlight_red%28+5+%29%2Bx%2Bx%2F2=40.
Moved 5 to the right of expression
It becomes x%2Bx%2Bx%2F2%2Bhighlight_green%28+5+%29=40.
Look at highlight_red%28+x+%29%2Bhighlight_red%28+x+%29%2Bhighlight_red%28+x%2F2+%29%2B5=40.
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+x+%29,highlight_red%28+x%2F2+%29 replacing them with highlight_green%28+%281%2B1%2B1%2F2%29%2Ax+%29
It becomes highlight_green%28+%281%2B1%2B1%2F2%29%2Ax+%29%2B5=40.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+5%2F2+%29%29%2Ax%2B5=40.
Look at highlight_red%28+%28highlight_red%28+5%2F2+%29%29%2Ax+%29%2B5=40.
Remove unneeded parentheses around factor highlight_red%28+5+%29,highlight_red%28+1%2F2+%29
It becomes highlight_green%28+5+%29%2Fhighlight_green%28+2+%29%2Ax%2B5=40.
Look at 5%2F2%2Ax%2B5=highlight_red%28+40+%29.
Moved these terms to the left highlight_green%28+-40+%29
It becomes 5%2F2%2Ax%2B5-highlight_green%28+40+%29=0.
Look at 5%2F2%2Ax%2Bhighlight_red%28+5+%29-highlight_red%28+40+%29=0.
Added fractions or integers together
It becomes 5%2F2%2Ax%2Bhighlight_green%28+-35+%29=0.
Look at 5%2F2%2Ax%2Bhighlight_red%28+-35+%29=0.
Removed extra sign in front of -35
It becomes 5%2F2%2Ax-highlight_green%28+35+%29=0.
Look at highlight_red%28+5%2F2%2Ax-35+%29=0.
Solved linear equation highlight_red%28+5%2F2%2Ax-35=0+%29 equivalent to 2.5*x-35 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=14.

Universal Simplifier and Solver


Done!



With x=14, then 5+x=19 and x/2=14/2=7.

Step 3. ANSWER: The numbers are 14, 19, and 7.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of thre numbers is 40. One number is 5 more than the second number. It is twice the third number. What are the numbers.

Let the second number be S
Then the first number is S + 5 since it is given that it's 5 more than the second number

And, since it's given that the 1st number is also twice the 3rd number, then the 3rd number = %28S+%2B+5%29%2F2

Since it's also given that the 3 numbers total 40, then we'll have: S+%2B+S+%2B+5+%2B+%28S+%2B+5%29%2F2+=+40

2S + 2S + 10 + S + 5 = 80 ------- Multiplying by LCD, 2

5S + 15 = 80

5S = 65

S+=+65%2F5+=+13

Therefore, the first number, or S + 5 is highlight_green%2818%29 (13 + 5), the second number, or S is highlight_green%2813%29, and the third highlight_green%289%29 (18%2F2).