SOLUTION: I really need some help with this problem, if anyone's not busy I would appreciate any help at all.  a waitress sold 17 ribeye steak dinners and 20 grilled salmon dinners, total

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Question 994723: I really need some help with this problem, if anyone's not busy I would appreciate any help at all.
 a waitress sold 17 ribeye steak dinners and 20 grilled salmon dinners, totalling $590.81 on a particular day. Another day she sold 24 ribeye steak dinners and 10 grilled salmon dinners, totaling $580.66. How much did each type of dinner cost?
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a waitress sold 17 ribeye steak dinners and 20 grilled salmon dinners, totalling $590.81 on a particular day. Another day she sold 24 ribeye steak dinners and 10 grilled salmon dinners, totaling $580.66. How much did each type of dinner cost?
------------
17r + 20s = 59081
24r + 10s = 58066 x2 --> 48r + 20s = 116132
----
17r + 20s = 59081
48r + 20s = 116132
-------------------------- Subtract
-31r = -57051
r = 1840.355 --> $18.40
Can you solve for s?

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let ribeye steak dinners be x and grilled salmon dinners y
if a waitress sold 17 ribeye steak dinners and 20 grilled salmon dinners, totaling $590.81 on a particular day, then we have
17x%2B20y=590.81.........eq.1
if another day she sold 24 ribeye steak dinners and 10 grilled salmon dinners, totaling $580.66, then we have
24x%2B10y=580.66.........eq.2
solve the system:
17x%2B20y=590.81.........eq.1
24x%2B10y=580.66.........eq.2...=> both sides multiply by 2
-------------------------------------------
17x%2B20y=590.81.........eq.1
48x%2B20y=1161.32.........eq.2=> subtract eq.1 from eq.2
-----------------------------------------------------
48x%2B20y-%2817x%2B20y%29=1161.32-590.81
48x%2Bcross%2820y%29-17x-cross%2820y%29=570.51
48x-17x=570.51
31x=570.51
x=570.51%2F31
x=18.40354838709677
highlight%28x=18.40%29
now find y
24x%2B10y=580.66.........eq.2
24%2A18.40354838709677%2B10y=580.66
441.68516129032248%2B10y=580.66
10y=580.66-441.68516129032248
10y=138.97483870967752
y=138.97%2F10
highlight%28y=13.89%29
How much did each type of dinner cost?
ribeye steak dinners cost highlight%2818.40%29 and
grilled salmon dinners cost highlight%2813.89%29