Question

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?

Answer 1



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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!

Answer 2

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

Explanation:

Let Cost of ribeye steaks dinners be x

Let Cost of grilled salmon dinners be y

So, According to question,

`15x+16y=597.21\\22x+8y=582.52`

`\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`

So, our equation becomes,

`\begin{bmatrix}330x+352y=13138.6\\\\ 330x+120y=8737.8\end{bmatrix}`

Now, we will use "Elimination method":

`330x+120y=8737.8\\\\-\\\\\underline{330x+352y=13138.6}\\\\\ -232y=-4400.8\\\\y=(4400.8)/(232)\\\\y=18.969`

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

`15x+16y=597.21\\\\15x+16* 18.969=597.21\\\\15x+303.504=597.21\\\\15x=597.21-303.504\\\\15x=293.706\\\\x=(293.706)/(15)\\\\x=19.58`

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