SOLUTION: For the Mr. Arlington contest, there were 206 more tickets sold at the door than were sold in advance. The tickets sold at the door cost $10 and the tickets sold in advance cost $6

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: For the Mr. Arlington contest, there were 206 more tickets sold at the door than were sold in advance. The tickets sold at the door cost $10 and the tickets sold in advance cost $6      Log On


   

Question 214817: For the Mr. Arlington contest, there were 206 more tickets sold at the door than were sold in advance. The tickets sold at the door cost $10 and the tickets sold in advance cost $6. The total amount of sales for both types of tickets was $6828. How many of each type of ticket was sold?

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
For the Mr. Arlington contest, there were 206 more tickets sold at the door than were sold in advance. The tickets sold at the door cost $10 and the tickets sold in advance cost $6. The total amount of sales for both types of tickets was $6828. How many of each type of ticket was sold?

Step 1. Let x be the number of tickets sold in advance.

Step 2. Let x+206 be the number of tickets sold at the door.

Step 3. Let 6x be the cost of the tickets sold in advance.

Step 4. Let 10(x+206) be the cost of the tickets sold at the door.

Step 5. Then 6x+10(x+206)=6828 be the cost of the total tickets sold.

Step 6. The following steps will solve the equation in Step 5.

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


YOUR ANSWER


  • This is an equation! Solutions: x=298.
  • Graphical form: Equation 6x%2B10%2A%28x%2B206%29=6828 was fully solved.
  • Text form: 6x+10*(x+206)=6828 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+6x%2B10%2A%28x%2B206%29=6828+%29
    For tutors: simplify_cartoon( 6x+10*(x+206)=6828 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 6%2Ax%2B10%2A%28x%2B206%29=highlight_red%28+6828+%29.
Moved these terms to the left highlight_green%28+-6828+%29
It becomes 6%2Ax%2B10%2A%28x%2B206%29-highlight_green%28+6828+%29=0.
Look at 6%2Ax%2Bhighlight_red%28+10%2A%28x%2B206%29+%29-6828=0.
Expanded term 10 by using associative property on %28x%2B206%29
It becomes 6%2Ax%2Bhighlight_green%28+10%2Ax+%29%2Bhighlight_green%28+10%2A206+%29-6828=0.
Look at 6%2Ax%2B10%2Ax%2Bhighlight_red%28+10+%29%2Ahighlight_red%28+206+%29-6828=0.
Multiplied numerator integers
It becomes 6%2Ax%2B10%2Ax%2Bhighlight_green%28+2060+%29-6828=0.
Look at 6%2Ax%2B10%2Ax%2Bhighlight_red%28+2060+%29-highlight_red%28+6828+%29=0.
Added fractions or integers together
It becomes 6%2Ax%2B10%2Ax%2Bhighlight_green%28+-4768+%29=0.
Look at 6%2Ax%2B10%2Ax%2Bhighlight_red%28+-4768+%29=0.
Removed extra sign in front of -4768
It becomes 6%2Ax%2B10%2Ax-highlight_green%28+4768+%29=0.
Look at highlight_red%28+6%2Ax+%29%2Bhighlight_red%28+10%2Ax+%29-4768=0.
Eliminated similar terms highlight_red%28+6%2Ax+%29,highlight_red%28+10%2Ax+%29 replacing them with highlight_green%28+%286%2B10%29%2Ax+%29
It becomes highlight_green%28+%286%2B10%29%2Ax+%29-4768=0.
Look at %28highlight_red%28+6+%29%2Bhighlight_red%28+10+%29%29%2Ax-4768=0.
Added fractions or integers together
It becomes %28highlight_green%28+16+%29%29%2Ax-4768=0.
Look at highlight_red%28+%28highlight_red%28+16+%29%29%2Ax+%29-4768=0.
Remove unneeded parentheses around factor highlight_red%28+16+%29
It becomes highlight_green%28+16+%29%2Ax-4768=0.
Look at highlight_red%28+16%2Ax-4768+%29=0.
Solved linear equation highlight_red%28+16%2Ax-4768=0+%29 equivalent to 16*x-4768 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=298.

Universal Simplifier and Solver


Done!



With x=298 , then x+206=298+206=504

Step 7. The number of tickets sold in advance is 298 and the number of tickets sold at the door is 504.

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