.
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.