SOLUTION: the sum of two numbers is 42. If the larger number is 3 more than triple the number find both numbers

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Question 225987: the sum of two numbers is 42. If the larger number is 3 more than triple the number find both numbers
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of two numbers is 42. If the larger number is 3 more than triple the number find both numbers

Step 1. Let x be the larger number.

Step 2. Let 42-x be the other and smaller number.

Step 3. Then, x=3+3(42-x) where I assume you meant the larger number is 3 more than triple the smaller number.

Step 4. Solving the equation in Step 3 yields the following steps

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


YOUR ANSWER


  • This is an equation! Solutions: x=32.25.
  • Graphical form: Equation x=3%2B3%2A%2842-x%29 was fully solved.
  • Text form: x=3+3*(42-x) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x=3%2B3%2A%2842-x%29+%29
    For tutors: simplify_cartoon( x=3+3*(42-x) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x=3%2B3%2A%28highlight_red%28+42+%29-x%29.
Moved 42 to the right of expression
It becomes x=3%2B3%2A%28-x%2Bhighlight_green%28+42+%29%29.
Look at x=highlight_red%28+3+%29%2B3%2A%28-x%2B42%29.
Moved 3 to the right of expression
It becomes x=3%2A%28-x%2B42%29%2Bhighlight_green%28+3+%29.
Look at x=highlight_red%28+3%2A%28-x%2B42%29%2B3+%29.
Moved these terms to the left highlight_green%28+-3%2A%28-x%2B42%29+%29,highlight_green%28+-3+%29
It becomes x-highlight_green%28+3%2A%28-x%2B42%29+%29-highlight_green%28+3+%29=0.
Look at x-highlight_red%28+3%2A%28-x%2B42%29+%29-3=0.
Expanded term -3 by using associative property on %28-x%2B42%29
It becomes x%2Bhighlight_green%28+3%2Ax+%29-highlight_green%28+3%2A42+%29-3=0.
Look at x%2B3%2Ax-highlight_red%28+3+%29%2Ahighlight_red%28+42+%29-3=0.
Multiplied numerator integers
It becomes x%2B3%2Ax-highlight_green%28+126+%29-3=0.
Look at x%2B3%2Ax-highlight_red%28+126+%29-highlight_red%28+3+%29=0.
Added fractions or integers together
It becomes x%2B3%2Ax%2Bhighlight_green%28+-129+%29=0.
Look at x%2B3%2Ax%2Bhighlight_red%28+-129+%29=0.
Removed extra sign in front of -129
It becomes x%2B3%2Ax-highlight_green%28+129+%29=0.
Look at highlight_red%28+x+%29%2Bhighlight_red%28+3%2Ax+%29-129=0.
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+3%2Ax+%29 replacing them with highlight_green%28+%281%2B3%29%2Ax+%29
It becomes highlight_green%28+%281%2B3%29%2Ax+%29-129=0.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+3+%29%29%2Ax-129=0.
Added fractions or integers together
It becomes %28highlight_green%28+4+%29%29%2Ax-129=0.
Look at highlight_red%28+%28highlight_red%28+4+%29%29%2Ax+%29-129=0.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes highlight_green%28+4+%29%2Ax-129=0.
Look at highlight_red%28+4%2Ax-129+%29=0.
Solved linear equation highlight_red%28+4%2Ax-129=0+%29 equivalent to 4*x-129 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=32.25.

Universal Simplifier and Solver


Done!



Let x=32.25, then 42-32.25=9.75. Check if equation is satisfied in Step 3.

32.25=3+3*9.75 which is a true statement.

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.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV