SOLUTION: 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

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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?

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
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?

Step 1. Let x be the number of hot dogs sold.

Step 2. Let 1300-x be the number of hamburgers sold

Step 3. Let 0.59x be the total cost of hot dogs sold.

Step 4. Let 0.98(1300-x) be the total cost of hamburgers sold.

Step 5. Let $1041.37-$79.37=$962 be the cost of the total bill before taxes.

Step 6. Then, 0.59x+0.98(1300-x)=962. Total cost of the bill before taxes.

Step 7. The following will solve the equation in Step 6.

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


YOUR ANSWER


  • 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.

DETAILED EXPLANATION

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.
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.
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.
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.
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.
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.
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.
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.
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
This is an equation! Solutions: x=800.

Universal Simplifier and Solver


Done!



With x=800 , then 1300-x=1300-800=500 .

Step 8. ANSWER: The number of hot dogs sold is 800 and the number of hamburgers sold is 500.

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