Question

Would each situation be represented by a positive or a negative number?

Answer 1

If 2 sodas and 4 hamburgers are $12.00 and 4 sodas and 2 hamburgers are $9.00 how much is a single hamburger?
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2s + 4h = 12, (1) 4s + 2h = 9. (2) Multiply (1) by 2. You will get 4s + 8h = 24, (1') 4s + 2h = 9. (2') Distract (2') from (1'). You will get 8h - 2h = 24 - 9, or 6h = 15 ---> h =  =  = 2.5. Thus one hamburger price is $2.50. Then from (1) s =  = 1. Answer. One hamburger price is $2.50 and 1 soda costs $1.00.

There is even more elegant way to solve the problem. 

Simply add all hamburgers and all sodas. 6 hamburgers and 6 sodas. $12 + $9 = $21. 

Hence, 1 hamburger + 1 soda =  = $3.50. 

Having this, everybody can solve to the end in this way, actually, without equations and using the mental math only. 


Question: A man measures the angle of elevation to the top of a mountain to be 12 degrees. He drives 7 miles closer and finds the angle of elevation to be 37 degrees. How high is the mountain?