SOLUTION: one number is 3 more than twice a second number. their sum is 27. find the numbers. (write an equation for this problem)

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Question 221471: one number is 3 more than twice a second number. their sum is 27. find the numbers. (write an equation for this problem)
Found 2 solutions by jim_thompson5910, drj:
Answer by jim_thompson5910(14901) About Me  (Show Source):
You can put this solution on YOUR website!
"one number is 3 more than twice a second number" means that y=2x%2B3


"their sum is 27" means x%2By=27


x%2By=27 Start with the 2nd equation


x%2B2x%2B3=27 Plug in y=2x%2B3


3x%2B3=27 Combine like terms on the left side.


3x=27-3 Subtract 3 from both sides.


3x=24 Combine like terms on the right side.


x=%2824%29%2F%283%29 Divide both sides by 3 to isolate x.


x=8 Reduce.


y=2x%2B3 Move onto to the 1st equation


y=2%288%29%2B3 Plug in x=8


y=16%2B3 Multiply.


y=19 Combine like terms on the right side.


So the two numbers are 8 and 19

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
One number is 3 more than twice a second number. Their sum is 27. Find the numbers. (Write an equation for this problem)

Step 1. Let m be the second number

Step 2. Let 2m+3 be the one number since it's 3 more than twice a second number.

Step 3. Then m+2m+3=27 since their sum is 27.

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

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:
Simplify m+2m+3=27
Your Answer:
  • Solutions: m=8.
  • Graphical form: Equation m%2B2m%2B3=27 was fully solved.
  • Text form: m+2m+3=27 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+m%2B2m%2B3=27+%29
    simplify_cartoon( m+2m+3=27 )

Detailed explanation:

Look at highlight_red%28+m+%29%2Bhighlight_red%28+2%2Am+%29%2B3=27.
Eliminated similar terms highlight_red%28+m+%29,highlight_red%28+2%2Am+%29 replacing them with highlight_green%28+%281%2B2%29%2Am+%29
It becomes highlight_green%28+%281%2B2%29%2Am+%29%2B3=27.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+2+%29%29%2Am%2B3=27.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2Am%2B3=27.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2Am+%29%2B3=27.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2Am%2B3=27.
Look at 3%2Am%2B3=highlight_red%28+27+%29.
Moved these terms to the left highlight_green%28+-27+%29
It becomes 3%2Am%2B3-highlight_green%28+27+%29=0.
Look at 3%2Am%2Bhighlight_red%28+3+%29-highlight_red%28+27+%29=0.
Added fractions or integers together
It becomes 3%2Am%2Bhighlight_green%28+-24+%29=0.
Look at 3%2Am%2Bhighlight_red%28+-24+%29=0.
Removed extra sign in front of -24
It becomes 3%2Am-highlight_green%28+24+%29=0.
Look at highlight_red%28+3%2Am-24+%29=0.
Solved linear equation highlight_red%28+3%2Am-24=0+%29 equivalent to 3*m-24 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
Solutions: m=8.

Done!



m=8 and 2m+3=19 and note that their sum is 27.

Step 5. ANSWER: The numbers are 19 and 8.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J