Question

Please help me solve this
a waitress sold 17 ribeye steak dinners and 10 grilled salmon dinners, totaling $580.22 on a particular day. Another day she sold 21 ribeye steak dinners and 5 grilled salmon dinners, totaling $582.19 how much did each type of dinner cost.

Answer 1

Answer:

$each \: ribeye \: costs \: \boxed{(r) \to \: \ 23.3664} ......................... .. \\ each \: grilled \: salmon \: dinners \: costs \: \boxed{(r) \to \: \ 18.29912}$

Step-by-step explanation:

$let \: ribeye \: be \to \: (r).......................... \\ let \: grilled \: salmon \: dinners \: be \to \: (g) \\ \tt{hence} \to\\ (5) \times 17r + 10g = \ 580.22 \\(10) \times 21r + 5g = \ 582.19 \\ \to \\ (85r + 50g = 2,901.1) \\ - (minus)\\ (210r + 50g =5,821.9 ) \\ - 125r = - 2,920.8 \\ r = \frac{ -2,920.8 }{ - 125} \\ \boxed{r = \ 23.3664} \\ \tt{hence} \to\\17r + 10g = \ 580.22 \\ 17(23.3664) + 10g = \ 580.22 \\1 0g = \ 580.22 - \ 397.2288 \\ 10g = \ 182.9912 \\ g = \frac{\ 182.9912}{10} \\ \boxed{g = \ 18.29912}$