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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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      Log On


   

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) About Me  (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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