SOLUTION: The owner of the Most Amazing Circus was counting the money from one day’s ticket sales. He knew that a total of 522 tickets were sold. Adult tickets cost $15 each and children’s

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The owner of the Most Amazing Circus was counting the money from one day’s ticket sales. He knew that a total of 522 tickets were sold. Adult tickets cost $15 each and children’s       Log On


   

Question 214818: The owner of the Most Amazing Circus was counting the money from one day’s ticket sales. He knew that a total of 522 tickets were sold. Adult tickets cost $15 each and children’s tickets cost $8 each. If the total receipts for the day were $5086.00, how many of each kind of ticket were sold?

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The owner of the Most Amazing Circus was counting the money from one day’s ticket sales. He knew that a total of 522 tickets were sold. Adult tickets cost $15 each and children’s tickets cost $8 each. If the total receipts for the day were $5086.00, how many of each kind of ticket were sold?

Step 1. Let x be the number of adult tickets sold.

Step 2. Let 522-x be the number of children tickets sold.

Step 3. let 15x be the total cost of adult tickets sold.

Step 4. Let 8(522-x) be the total cost of children tickets sold.

Step 5. Then 15x+8*(522-x)=5086 is the total cost of tickets sold

Step 6. The following 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=130.
  • Graphical form: Equation 15x%2B8%2A%28522-x%29=5086 was fully solved.
  • Text form: 15x+8*(522-x)=5086 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+15x%2B8%2A%28522-x%29=5086+%29
    For tutors: simplify_cartoon( 15x+8*(522-x)=5086 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 15%2Ax%2B8%2A%28highlight_red%28+522+%29-x%29=5086.
Moved 522 to the right of expression
It becomes 15%2Ax%2B8%2A%28-x%2Bhighlight_green%28+522+%29%29=5086.
Look at 15%2Ax%2B8%2A%28-x%2B522%29=highlight_red%28+5086+%29.
Moved these terms to the left highlight_green%28+-5086+%29
It becomes 15%2Ax%2B8%2A%28-x%2B522%29-highlight_green%28+5086+%29=0.
Look at 15%2Ax%2Bhighlight_red%28+8%2A%28-x%2B522%29+%29-5086=0.
Expanded term 8 by using associative property on %28-x%2B522%29
It becomes 15%2Ax-highlight_green%28+8%2Ax+%29%2Bhighlight_green%28+8%2A522+%29-5086=0.
Look at 15%2Ax-8%2Ax%2Bhighlight_red%28+8+%29%2Ahighlight_red%28+522+%29-5086=0.
Multiplied numerator integers
It becomes 15%2Ax-8%2Ax%2Bhighlight_green%28+4176+%29-5086=0.
Look at 15%2Ax-8%2Ax%2Bhighlight_red%28+4176+%29-highlight_red%28+5086+%29=0.
Added fractions or integers together
It becomes 15%2Ax-8%2Ax%2Bhighlight_green%28+-910+%29=0.
Look at 15%2Ax-8%2Ax%2Bhighlight_red%28+-910+%29=0.
Removed extra sign in front of -910
It becomes 15%2Ax-8%2Ax-highlight_green%28+910+%29=0.
Look at highlight_red%28+15%2Ax+%29-highlight_red%28+8%2Ax+%29-910=0.
Eliminated similar terms highlight_red%28+15%2Ax+%29,highlight_red%28+-8%2Ax+%29 replacing them with highlight_green%28+%2815-8%29%2Ax+%29
It becomes highlight_green%28+%2815-8%29%2Ax+%29-910=0.
Look at %28highlight_red%28+15+%29-highlight_red%28+8+%29%29%2Ax-910=0.
Added fractions or integers together
It becomes %28highlight_green%28+7+%29%29%2Ax-910=0.
Look at highlight_red%28+%28highlight_red%28+7+%29%29%2Ax+%29-910=0.
Remove unneeded parentheses around factor highlight_red%28+7+%29
It becomes highlight_green%28+7+%29%2Ax-910=0.
Look at highlight_red%28+7%2Ax-910+%29=0.
Solved linear equation highlight_red%28+7%2Ax-910=0+%29 equivalent to 7*x-910 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=130.

Universal Simplifier and Solver


Done!



With x=130 adult tickets sold then 522-x=522-130=392 children tickets sold.

Step 7. ANSWER: The number of adult tickets sold is 130 and the number of children tickets sold is 392.

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