Answer:
- steak: $17.41
- salmon: $26.06
Explanation:
You want to know the cost of each type of dinner when 12 steak dinners and 15 salmon dinners were sold for $599.82, and 26 steak dinners and 5 salmon dinners were sold for $582.96.
Setup
The two sales can be written as equations, where x is the cost of a steak dinner and y is the cost of a salmon dinner:
12x +15y = 599.82
26x +5y = 582.96
Solution
We can solve this system of equations by elimination. Subtracting the first equation from 3 times the second gives ...
3(26x +5y) -(12x +15y) = 3(582.96) -(599.82)
66x = 1149.06 . . . . simplify
x = 17.41 . . . . . . . . . divide by 66
Substituting for x in the first equation, we have ...
12(17.41) +15y = 599.82
15y = 390.90 . . . . . . . . . subtract 208.92
y = 26.06 . . . . . . . . . . . divide by 15
A ribeye steak dinner costs $17.41, and a grilled salmon dinner costs $26.06.
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Additional comment
The problem statement here gives the second dinner value as $582.98. We believe that is a typo, as the resulting individual dinner costs do not come out to whole cents that way. That is why we have used the value $582.96 instead.