Question

Your family goes to a southern style restaurant for dinner. there are 6 total people in your family. some order chicken for $14 and the rest order steak for $17. the total bill is $99. which system could be used to determine the number of chicken dinners (c) and steak dinners (s) ordered?

Answer 1

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Define x and y:
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Let c be the number of people that ordered chickens.
Let s be the number of people that ordered steak.

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Construct the equations:
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There are 6  people in all.
c + s = 6

Chicken cost $14 and Steak costs $17. The total bill is $99.
14c + 17s = 99

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Solve c and s:
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c + s = 6                  --------------------- (1)
14c + 17s = 99        --------------------- (2)

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From equation 1:
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c + s = 6
c = 6 - s

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Sub c = 6 - s into equation 2:
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14 (6 - s) + 17s = 99
84 - 14s + 17s = 99
84 + 3s = 99
3s = 99 - 84
3s = 15
s = 5

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Sub s = 5 into equation 1:
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c + s = 6
c + 5 = 6
c = 6 - 5
c = 1

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Answer: 1 person ordered the chicken and 5 people ordered the steak.
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