SOLUTION: The sum of two numbers is twelve. The total of three times the smaller number and six amounts to seven less than the product of four and the larger number. Find the two numbers.

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Question 223660: The sum of two numbers is twelve. The total of three times the smaller number and six amounts to seven less than the product of four and the larger number. Find the two numbers.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of two numbers is twelve. The total of three times the smaller number and six amounts to seven less than the product of four and the larger number. Find the two numbers.

Step 1. Let x be one number

Step 2. Let 12-x be the other number

Step 3. 3x+6=4*(12-x)-7 since the total of three times the smaller number and six amounts to seven less than the product of four and the larger number.

Step 4. Solving yields the following steps

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


YOUR ANSWER


  • This is an equation! Solutions: x=5.
  • Graphical form: Equation 3x%2B6=4%2A%2812-x%29-7 was fully solved.
  • Text form: 3x+6=4*(12-x)-7 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+3x%2B6=4%2A%2812-x%29-7+%29
    For tutors: simplify_cartoon( 3x+6=4*(12-x)-7 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 3%2Ax%2B6=4%2A%28highlight_red%28+12+%29-x%29-7.
Moved 12 to the right of expression
It becomes 3%2Ax%2B6=4%2A%28-x%2Bhighlight_green%28+12+%29%29-7.
Look at 3%2Ax%2B6=highlight_red%28+4%2A%28-x%2B12%29-7+%29.
Moved these terms to the left highlight_green%28+-4%2A%28-x%2B12%29+%29,highlight_green%28+7+%29
It becomes 3%2Ax%2B6-highlight_green%28+4%2A%28-x%2B12%29+%29%2Bhighlight_green%28+7+%29=0.
Look at 3%2Ax%2Bhighlight_red%28+6+%29-4%2A%28-x%2B12%29%2Bhighlight_red%28+7+%29=0.
Added fractions or integers together
It becomes 3%2Ax%2Bhighlight_green%28+13+%29-4%2A%28-x%2B12%29=0.
Look at 3%2Ax%2Bhighlight_red%28+13+%29-4%2A%28-x%2B12%29=0.
Moved 13 to the right of expression
It becomes 3%2Ax-4%2A%28-x%2B12%29%2Bhighlight_green%28+13+%29=0.
Look at 3%2Ax-highlight_red%28+4%2A%28-x%2B12%29+%29%2B13=0.
Expanded term -4 by using associative property on %28-x%2B12%29
It becomes 3%2Ax%2Bhighlight_green%28+4%2Ax+%29-highlight_green%28+4%2A12+%29%2B13=0.
Look at 3%2Ax%2B4%2Ax-highlight_red%28+4+%29%2Ahighlight_red%28+12+%29%2B13=0.
Multiplied numerator integers
It becomes 3%2Ax%2B4%2Ax-highlight_green%28+48+%29%2B13=0.
Look at 3%2Ax%2B4%2Ax-highlight_red%28+48+%29%2Bhighlight_red%28+13+%29=0.
Added fractions or integers together
It becomes 3%2Ax%2B4%2Ax%2Bhighlight_green%28+-35+%29=0.
Look at 3%2Ax%2B4%2Ax%2Bhighlight_red%28+-35+%29=0.
Removed extra sign in front of -35
It becomes 3%2Ax%2B4%2Ax-highlight_green%28+35+%29=0.
Look at highlight_red%28+3%2Ax+%29%2Bhighlight_red%28+4%2Ax+%29-35=0.
Eliminated similar terms highlight_red%28+3%2Ax+%29,highlight_red%28+4%2Ax+%29 replacing them with highlight_green%28+%283%2B4%29%2Ax+%29
It becomes highlight_green%28+%283%2B4%29%2Ax+%29-35=0.
Look at %28highlight_red%28+3+%29%2Bhighlight_red%28+4+%29%29%2Ax-35=0.
Added fractions or integers together
It becomes %28highlight_green%28+7+%29%29%2Ax-35=0.
Look at highlight_red%28+%28highlight_red%28+7+%29%29%2Ax+%29-35=0.
Remove unneeded parentheses around factor highlight_red%28+7+%29
It becomes highlight_green%28+7+%29%2Ax-35=0.
Look at highlight_red%28+7%2Ax-35+%29=0.
Solved linear equation highlight_red%28+7%2Ax-35=0+%29 equivalent to 7*x-35 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=5.

Universal Simplifier and Solver


Done!



With x=5, then 12-5=7

Check...3x%2B6=4%2A%2812-x%29-7 or 3%2A5%2B6=4%2A7-7 which is a true statement.

Step 5. ANSWER: The numbers are 5 and 7


I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J