Question 1034736
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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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<pre>
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 = {{{15/6}}} = {{{5/2}}} = 2.5.


Thus one hamburger price is $2.50.

Then from (1)  s = {{{(12-4*2.50)/2}}} = 1.

<U>Answer</U>. One hamburger price is $2.50 and 1 soda costs $1.00.
</pre>


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 = {{{21/6}}} = $3.50.


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