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

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) (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 was fully solved.
Text form: 0.59x+0.98*(1300-x)=962 simplifies to 0=0
Cartoon (animation) form:
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 .
Moved 1300

to the right of expression
It becomes .

Look at .
Moved these terms to the left highlight_green%28+-962+%29

It becomes .

Look at .
Expanded term 0.98

by using associative property on %28-x%2B1300%29

It becomes .

Look at .
Replace constants in expression: highlight_red%28+0.98%2A1300+%29

with

It becomes .

Look at .
Moved 312

to the right of expression
It becomes .

Look at .
Eliminated similar terms highlight_red%28+0.59%2Ax+%29

replacing them with highlight_green%28+%280.59-0.98%29%2Ax+%29

It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Remove unneeded parentheses around factor highlight_red%28+39+%29

It becomes .

Look at .
Solved linear equation highlight_red%28+-39%2F100%2Ax%2B312=0+%29

equivalent to -0.39*x+312 =0
It becomes .
Result:
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

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