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PLEASE HELP ME!

Suppose that Kristin placed an order for five hamburgers and two sodas, for a total of 1781 calories. Jake placed an order for seven hamburgers and five sodas, for a total of 2940 calories. How many calories are in a hamburger? How many calories are in a soda?

Respuesta :

the soda has "s" calories

s = calories in a soda
h = calories in a hamburger

[tex]\bf \begin{array}{lccclll} &hamburgers&sodas&calories\\ &-----&-----&-----\\ Kristin&5h&2s&1781\\ Jake&7h&5s&2940 \end{array}\\\\ -----------------------------\\\\ thus\qquad \begin{cases} 5h+2s=1781\implies 5h=1781-2s\\\\ \qquad \boxed{h}=\frac{1781-2s}{5}\\\\ 7h+5s=2940\\ ----------\\ 7\left( \boxed{\frac{1781-2s}{5}} \right)+5s=2940 \end{cases}[/tex]

solve for "s"
Setup:
5h + 2s = 1781 - multiply by 5
7h + 5s = 2940 - multiply by -2

25h + 10s = 8905
-14h - 10s = -5880 - add the two equations together

11h = 3025
h = 275 calories for hamburger

Plug back in
5(275) + 2s = 1781
1375 + 2s = 1781
2s = 406
s = 203 calories of soda

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