How
Many tress there were a long time ago
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?
Step-by-step explanation:
the lines are all going through the origin (0, 0), so the y-intercept is the same (0) for all 4.
therefore, we only need to focus on the slope of the lines to see which two are identical.
the slope is the ratio "y coordinate change / x coordinate change" when going from one point to another on the line.
one point is for all 4 lines the origin, so the coordinate changes are the point coordinates themselves, and we only need to calculate y/x and see, which ones are equal.
105/15 = 7/1 = 7
150/12 = 50/4 = 25/2 = 12.5
120/10 = 12
96/8 = 12
so, C and D have identical slopes and therefore identical graphs, and have therefore the same costs of T-shirts.
