If 2 sodas and 4 hamburgers are $12.00 and 4 sodas and 2 hamburgers are $9.00 how much is a single hamburger?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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?
The pattern is dividing by 2.
512, 256, 128, 64
512/2 = 256, 256/2 = 128, 128/2 = 64
64/2 = 32, 32/2 = 16, 16/2 = 8, 8/2 = 4, 4/2 = 2, ...
if you are looking for the slope the answer would be y=4/7x+25/7
