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A waitress sold 15 ribeye steaks dinners and 16 grilled salmon dinners, totaling $597.21 on a particular day. Another day, she sold 22 ribeye steak dinners and 8 grilled salmon dinners, totaling $582.52 how much did each type of dinner cost?

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Answer: Cost of ribeye steaks dinners be $19.58 and Cost of grilled salmon dinners be $18.969.

Step-by-step explanation:

Let Cost of ribeye steaks dinners be x

Let Cost of grilled salmon dinners be y

So, According to question,

[tex]15x+16y=597.21\\22x+8y=582.52[/tex]

[tex]\mathrm{Multiply\:}15x+16y=597.21\mathrm{\:by\:}22:\quad 330x+352y=13138.6\\\\\mathrm{Multiply\:}22x+8y=582.52\mathrm{\:by\:}15:\quad 330x+120y=8737.8[/tex]

So, our equation becomes,

[tex]\begin{bmatrix}330x+352y=13138.6\\\\ 330x+120y=8737.8\end{bmatrix}[/tex]

Now, we will use "Elimination method":

[tex]330x+120y=8737.8\\\\-\\\\\underline{330x+352y=13138.6}\\\\\ -232y=-4400.8\\\\y=\frac{4400.8}{232}\\\\y=18.969[/tex]

Now, put the value of y in any one of the equation:

[tex]15x+16y=597.21\\\\15x+16\times 18.969=597.21\\\\15x+303.504=597.21\\\\15x=597.21-303.504\\\\15x=293.706\\\\x=\frac{293.706}{15}\\\\x=19.58[/tex]

Hence , Cost of ribeye steaks dinners be $19.58 and Cost of grilled salmon dinners be $18.969.

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Sam F.

 asked • 10/19/15

word problem

A waitress sold 13 ribeye steak dinners and 18 grilled salmon dinners, totaling $550.25 on a particular day. Another day she sold 22 ribeye steak dinners and 6 grilled salmon dinners, totaling $582.08. How much did each type of dinner.

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Rishi M. answered • 10/19/15

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This is a systems of equations question.  Let's set ribeye steak to the variable r, and grilled salmon to s.

 

We get these two equations:

13r + 18s = 550.25

22r + 6s = 582.08

 

First, we'll isolate one variable in the first equation.  Let's choose r:

13r = 550.25 - 18s

r = 42.33 - 1.38s

 

Now, we'll take this value for r and plug it into the second equation:

22r + 6s = 582.08

22 (42.33 - 1.38s) + 6s = 582.08

(931.19 - 30.46s) + 6s = 582.08          | multiply values by 22

931.19 - 24.46s = 582.08                   | combine s values

349.11 = 24.46s                               | move 582.08 to left side, and combine;  move -24.46s to right side

14.27 = s                                        | solve for s

 

Now, plug this value for s back into the first equation:

13r + 18s = 550.25

13r + 18 (14.27) = 550.25

13r = 256.91 = 550.25

13r = 293.34

r = 22.56

 

So r = 22.56 and s = 14.27.

 

The ribeye steak dinners cost $22.56 each and the grilled salmon dinners cost $14.27 each.

 

Note, this solution does not factor in any tips the waitress makes on each dinner!

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