SOLUTION: If 3 is added to a number and the sum is tripled, the result is 27 more than the number. The number is ?

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Question 211881: If 3 is added to a number and the sum is tripled, the result is 27 more than the number.
The number is ?
Found 3 solutions by marcsam823, gypsy1274, ankor@dixie-net.com:
Answer by marcsam823(57) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the number
Now break the sentence into parts and translate the words into an algebraic expression:
a) If 3 is added to the number: x + 3
b) ...and the sum is tripled..
"The sum" is "x + 3" so: 3(x+3)
c) ...the result is 27 more than the number.
27 more than the number is x + 27
d) Put it all together:
3(x + 3) = x + 27
Solve for x:
1) Distribute the left side of the equation:
3x + 9 = x + 27
2) Subtract x from each side of the equation:
2x + 9 = 27
3) Subtract 9 from each side of the equation:
2x = 18
4) Solve for x:
x = 9
Check:
1) x = 9
2) 3(x + 3) = x + 27
3) 3 ([9] + 3) = [9] + 27
4) 3(12) = 9 + 27
5) 36 = 36
The answer is correct

Answer by gypsy1274(9) About Me  (Show Source):
You can put this solution on YOUR website!
Lets break this into pieces. "If three is added to a number..." Let the number be x and add three. x+3
"...the sum is tripled..." The x+3 should be added together before the multiplication is done so we need to use parenthesis to change the order of operations. 3*(x+3)
"...the result..." means we are finished with the left side of the equation and need to enter an =. So the equation starts out 3(x+3)=
"...is 27 more than the number." 27+x
Now we know what each side of the equation is so put it together and get:
3(x+3)=27+x
Next, solve for x.
Step 1. distribute
3x+9=27+x
Step 2. subtract x from both sides of the equation.
3x+9-x=27+x-x
Step 3. combine like terms.
2x+9=27
Step 4. subtract 9 from both sides of the equation.
2x+9-9=27-9
Step 5. combine like terms.
2x=18
Step 6. divide both sides by 2
2x/2=18/2
x=9
Or for a slightly different explaination:
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=9.
  • Graphical form: Equation 3%2A%28x%2B3%29=27%2Bx was fully solved.
  • Text form: 3*(x+3)=27+x simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+3%2A%28x%2B3%29=27%2Bx+%29
    For tutors: simplify_cartoon( 3*(x+3)=27+x )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 3%2A%28x%2B3%29=highlight_red%28+27+%29%2Bx.
Moved 27 to the right of expression
It becomes 3%2A%28x%2B3%29=x%2Bhighlight_green%28+27+%29.
Look at 3%2A%28x%2B3%29=highlight_red%28+x%2B27+%29.
Moved these terms to the left highlight_green%28+-x+%29,highlight_green%28+-27+%29
It becomes 3%2A%28x%2B3%29-highlight_green%28+x+%29-highlight_green%28+27+%29=0.
Look at highlight_red%28+3%2A%28x%2B3%29+%29-x-27=0.
Expanded term 3 by using associative property on %28x%2B3%29
It becomes highlight_green%28+3%2Ax+%29%2Bhighlight_green%28+3%2A3+%29-x-27=0.
Look at 3%2Ax%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+3+%29-x-27=0.
Multiplied numerator integers
It becomes 3%2Ax%2Bhighlight_green%28+9+%29-x-27=0.
Look at 3%2Ax%2Bhighlight_red%28+9+%29-x-highlight_red%28+27+%29=0.
Added fractions or integers together
It becomes 3%2Ax%2Bhighlight_green%28+-18+%29-x=0.
Look at 3%2Ax%2Bhighlight_red%28+-18+%29-x=0.
Moved -18 to the right of expression
It becomes 3%2Ax-x%2Bhighlight_green%28+-18+%29=0.
Look at 3%2Ax-x%2Bhighlight_red%28+-18+%29=0.
Removed extra sign in front of -18
It becomes 3%2Ax-x-highlight_green%28+18+%29=0.
Look at highlight_red%28+3%2Ax+%29-highlight_red%28+x+%29-18=0.
Eliminated similar terms highlight_red%28+3%2Ax+%29,highlight_red%28+-x+%29 replacing them with highlight_green%28+%283-1%29%2Ax+%29
It becomes highlight_green%28+%283-1%29%2Ax+%29-18=0.
Look at %28highlight_red%28+3+%29-highlight_red%28+1+%29%29%2Ax-18=0.
Added fractions or integers together
It becomes %28highlight_green%28+2+%29%29%2Ax-18=0.
Look at highlight_red%28+%28highlight_red%28+2+%29%29%2Ax+%29-18=0.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes highlight_green%28+2+%29%2Ax-18=0.
Look at highlight_red%28+2%2Ax-18+%29=0.
Solved linear equation highlight_red%28+2%2Ax-18=0+%29 equivalent to 2*x-18 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=9.

Universal Simplifier and Solver


Done!

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = "a number"
:
If 3 is added to a number and the sum is tripled, the result is 27 more than the number.
3(x+3) = x + 27
3x + 9 = x + 27
3x - x = 27 - 9
2x = 18
x = 18%2F2
x = 9 is the number
;
:
Check solution in the given statement:
3(9+3) = 9 + 27
3(12) = 36