If H and S represent the calorie content of hamburgers and sodas, respectively, then you have
.. 5H +2S = 1790
.. 2H +3S = 1178
By Cramer's rule, (Google it)
.. H = (2*1178 -3*1790)/(2*2 -3*5) = -3014/-11 = 274
.. S = (1790*2 -1178*5)/-11 = -2310/-11 = 210
There are 274 calories in a hamburger; 210 calories in a soda.
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Actually, the above solution is found using the methods of Vedic mathematics. The formula for
.. ax +by =c
.. dx +ey = f
is
.. x = (bf -ec)/(bd -ae) . . . . . . . the products are a simple crossing pattern
.. y = (cd -fa)/(same denominator)
The actual Cramer's Rule uses the negative of both numerator and denominator, that is (ce-bf)/(ae-bd) = x, for example. I find the Vedic pattern of products easier to remember.
As with most math problems, there are many ways to solve it. You are probably taught methods of elimination and substitution. Graphing works, too. (See the image.)
