SOLUTION: Please help! The caterers for a semi formal dinner and dance are preparing two different meals; chicken at 12$ or pasta at 8$. The total cost of the dinners for 240 students is $21

Question 1015089: Please help! The caterers for a semi formal dinner and dance are preparing two different meals; chicken at 12$ or pasta at 8$. The total cost of the dinners for 240 students is $2100.
A. Create a linear system to model this situation. Define your variables.
B. Solve the system to determine the number of chicken and pasta dinners the students ordered
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
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A. Create a linear system to model this situation. Define your variables.
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C=number of chicken plates; P=number of pasta plates
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C+P=240
$12C+$8P=$2100
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B. Solve the system to determine the number of chicken and pasta dinners the students ordered
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C+P=240
P=240-C . (Use this to substitute for P below)
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$12C+$8P=$2100 . (Substitute for P - see above)
$12C+$8(240-C)=$2100
$12C+$1920-$8C=$2100
$4C=$180
C=45
ANSWER 1: They ordered 45 chicken dinners.
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P=240-C=240-45=195
ANSWER 2: They ordered 195 pasta dinners.
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CHECK:
$12C+$8P=$2100
$12(45)+$8(195)=$2100
$540+$1560=$2100
$2100=$2100
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