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

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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)   (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 was fully solved.
  • Text form: 6x+2.5*(370-x)=1723 simplifies to 0=0
  • Cartoon (animation) form:
    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 .
Moved 370 to the right of expression
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-1723+%29
It becomes .
Look at .
Expanded term 2.5 by using associative property on %28-x%2B370%29
It becomes .
Look at .
Replace constants in expression: highlight_red%28+2.5%2A370+%29,highlight_red%28+-1723+%29 with highlight_green%28+-798+%29
It becomes .
Look at .
Moved -798 to the right of expression
It becomes .
Look at .
Removed extra sign in front of -798
It becomes .
Look at .
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 .
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+35+%29,highlight_red%28+1%2F10+%29
It becomes .
Look at .
Factors 35 and 10 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes .
Look at .
Solved linear equation highlight_red%28+7%2F2%2Ax-798=0+%29 equivalent to 3.5*x-798 =0
It becomes .
Result:
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
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