SOLUTION: Adult tickets for a play cost $6.00 and children's tickets cost $2.50. For one performance, 370 tickets were sold. Receipts for the performance were $1723. Find the number of adult

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: Adult tickets for a play cost $6.00 and children's tickets cost $2.50. For one performance, 370 tickets were sold. Receipts for the performance were $1723. Find the number of adult      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 223990: Adult tickets for a play cost $6.00 and children's tickets cost $2.50. For one performance, 370 tickets were sold. Receipts for the performance were $1723. Find the number of adult tickets sold.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Adult tickets for a play cost $6.00 and children's tickets cost $2.50. For one performance, 370 tickets were sold. Receipts for the performance were $1723. Find the number of adult tickets sold.

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

Step 2. Let 6x be the dollar value of adult tickets.

Step 3. Let 370-x be the number of children tickets.

Step 4. Let 2.5(370-x) be the dollar value of children tickets.

Step 5. Then, 6x+2.5(370-x)=1723 is the total dollar value.

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


YOUR ANSWER


  • This is an equation! Solutions: x=228.
  • Graphical form: Equation 6x%2B2.5%2A%28370-x%29=1723 was fully solved.
  • Text form: 6x+2.5*(370-x)=1723 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+6x%2B2.5%2A%28370-x%29=1723+%29
    For tutors: simplify_cartoon( 6x+2.5*(370-x)=1723 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 6%2Ax%2B2.5%2A%28highlight_red%28+370+%29-x%29=1723.
Moved 370 to the right of expression
It becomes 6%2Ax%2B2.5%2A%28-x%2Bhighlight_green%28+370+%29%29=1723.
Look at 6%2Ax%2B2.5%2A%28-x%2B370%29=highlight_red%28+1723+%29.
Moved these terms to the left highlight_green%28+-1723+%29
It becomes 6%2Ax%2B2.5%2A%28-x%2B370%29-highlight_green%28+1723+%29=0.
Look at 6%2Ax%2Bhighlight_red%28+2.5%2A%28-x%2B370%29+%29-1723=0.
Expanded term 2.5 by using associative property on %28-x%2B370%29
It becomes 6%2Ax-highlight_green%28+2.5%2Ax+%29%2Bhighlight_green%28+2.5%2A370+%29-1723=0.
Look at 6%2Ax-2.5%2Ax%2Bhighlight_red%28+2.5%2A370+%29-highlight_red%28+1723+%29=0.
Replace constants in expression: highlight_red%28+2.5%2A370+%29,highlight_red%28+-1723+%29 with highlight_green%28+-798+%29
It becomes highlight_green%28+-798+%29%2B6%2Ax-2.5%2Ax=0.
Look at highlight_red%28+-798+%29%2B6%2Ax-2.5%2Ax=0.
Moved -798 to the right of expression
It becomes 6%2Ax-2.5%2Ax%2Bhighlight_green%28+-798+%29=0.
Look at 6%2Ax-2.5%2Ax%2Bhighlight_red%28+-798+%29=0.
Removed extra sign in front of -798
It becomes 6%2Ax-2.5%2Ax-highlight_green%28+798+%29=0.
Look at highlight_red%28+6%2Ax+%29-highlight_red%28+2.5%2Ax+%29-798=0.
Eliminated similar terms highlight_red%28+6%2Ax+%29,highlight_red%28+-2.5%2Ax+%29 replacing them with highlight_green%28+%286-2.5%29%2Ax+%29
It becomes highlight_green%28+%286-2.5%29%2Ax+%29-798=0.
Look at %28highlight_red%28+6+%29-highlight_red%28+2.5+%29%29%2Ax-798=0.
Added fractions or integers together
It becomes %28highlight_green%28+35%2F10+%29%29%2Ax-798=0.
Look at highlight_red%28+%28highlight_red%28+35%2F10+%29%29%2Ax+%29-798=0.
Remove unneeded parentheses around factor highlight_red%28+35+%29,highlight_red%28+1%2F10+%29
It becomes highlight_green%28+35+%29%2Fhighlight_green%28+10+%29%2Ax-798=0.
Look at highlight_red%28+35+%29%2Fhighlight_red%28+10+%29%2Ax-798=0.
Factors 35 and 10 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes highlight_green%28+7+%29%2Fhighlight_green%28+2+%29%2Ax-798=0.
Look at highlight_red%28+7%2F2%2Ax-798+%29=0.
Solved linear equation highlight_red%28+7%2F2%2Ax-798=0+%29 equivalent to 3.5*x-798 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=228.

Universal Simplifier and Solver


Done!



Step 6. ANSWER; The number of adult tickets sold is 228.

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