document.write( "Question 214815: The Freshman class is organizing a picnic and ordered a total of 1300 hot dogs and hamburgers for the event. The hot dogs cost $0.59 each and the hamburgers cost $0.98 each before tax. The total bill came to $1041.37, which included $79.37 in tax. How many hot dogs and how many hamburgers were ordered? \r
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Algebra.Com's Answer #162285 by drj(1380) $\"\"$ $\"About$

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The Freshman class is organizing a picnic and ordered a total of 1300 hot dogs and hamburgers for the event. The hot dogs cost $0.59 each and the hamburgers cost $0.98 each before tax. The total bill came to $1041.37, which included $79.37 in tax. How many hot dogs and how many hamburgers were ordered?\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let x be the number of hot dogs sold.\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let 1300-x be the number of hamburgers sold\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let 0.59x be the total cost of hot dogs sold.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Let 0.98(1300-x) be the total cost of hamburgers sold.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. Let $1041.37-$79.37=$962 be the cost of the total bill before taxes.\r
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\n" ); document.write( "\n" ); document.write( "Step 6. Then, 0.59x+0.98(1300-x)=962. Total cost of the bill before taxes.\r
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\n" ); document.write( "\n" ); document.write( "Step 7. The following will solve the equation in Step 6.\r
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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This is an equation! Solutions: x=800.
Graphical form: Equation $\"0.59x%2B0.98%2A%281300-x%29=962\"$ was fully solved.
Text form: 0.59x+0.98*(1300-x)=962 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+0.59x%2B0.98%2A%281300-x%29=962+%29\"$
For tutors: simplify_cartoon( 0.59x+0.98*(1300-x)=962 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"0.59%2Ax%2B0.98%2A%28highlight_red%28+1300+%29-x%29=962\"$ .
Moved $\"1300\"$ to the right of expression
It becomes $\"0.59%2Ax%2B0.98%2A%28-x%2Bhighlight_green%28+1300+%29%29=962\"$ .
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Look at $\"0.59%2Ax%2B0.98%2A%28-x%2B1300%29=highlight_red%28+962+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-962+%29\"$
It becomes $\"0.59%2Ax%2B0.98%2A%28-x%2B1300%29-highlight_green%28+962+%29=0\"$ .
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Look at $\"0.59%2Ax%2Bhighlight_red%28+0.98%2A%28-x%2B1300%29+%29-962=0\"$ .
Expanded term $\"0.98\"$ by using associative property on $\"%28-x%2B1300%29\"$
It becomes $\"0.59%2Ax-highlight_green%28+0.98%2Ax+%29%2Bhighlight_green%28+0.98%2A1300+%29-962=0\"$ .
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Look at $\"0.59%2Ax-0.98%2Ax%2Bhighlight_red%28+0.98%2A1300+%29-highlight_red%28+962+%29=0\"$ .
Replace constants in expression: $\"highlight_red%28+0.98%2A1300+%29\"$ , $\"highlight_red%28+-962+%29\"$ with $\"highlight_green%28+312+%29\"$
It becomes $\"highlight_green%28+312+%29%2B0.59%2Ax-0.98%2Ax=0\"$ .
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Look at $\"highlight_red%28+312+%29%2B0.59%2Ax-0.98%2Ax=0\"$ .
Moved $\"312\"$ to the right of expression
It becomes $\"0.59%2Ax-0.98%2Ax%2Bhighlight_green%28+312+%29=0\"$ .
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Look at $\"highlight_red%28+0.59%2Ax+%29-highlight_red%28+0.98%2Ax+%29%2B312=0\"$ .
Eliminated similar terms $\"highlight_red%28+0.59%2Ax+%29\"$ , $\"highlight_red%28+-0.98%2Ax+%29\"$ replacing them with $\"highlight_green%28+%280.59-0.98%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%280.59-0.98%29%2Ax+%29%2B312=0\"$ .
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Look at $\"%28highlight_red%28+0.59+%29-highlight_red%28+0.98+%29%29%2Ax%2B312=0\"$ .
Added fractions or integers together
It becomes $\"%28-highlight_green%28+39%2F100+%29%29%2Ax%2B312=0\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+39%2F100+%29%29%2Ax+%29%2B312=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+39+%29\"$ , $\"highlight_red%28+1%2F100+%29\"$
It becomes $\"-highlight_green%28+39+%29%2Fhighlight_green%28+100+%29%2Ax%2B312=0\"$ .
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Look at $\"highlight_red%28+-39%2F100%2Ax%2B312+%29=0\"$ .
Solved linear equation $\"highlight_red%28+-39%2F100%2Ax%2B312=0+%29\"$ equivalent to -0.39*x+312 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: x=800.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "With x=800 , then 1300-x=1300-800=500 .\r
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\n" ); document.write( "\n" ); document.write( "Step 8. ANSWER: The number of hot dogs sold is 800 and the number of hamburgers sold is 500.\r
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\n" ); document.write( "\n" ); document.write( "I hope the above steps were helpful.\r
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\n" ); document.write( "\n" ); document.write( "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.\r
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\n" ); document.write( "\n" ); document.write( "Good luck in your studies!\r
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\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J\r
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