SOLUTION: A large group goes to a restaurant and orders chicken dinners for $8 and steak dinners for $9. If 27 people spend $235, how many have chicken and steak? How can I write a linear eq

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A large group goes to a restaurant and orders chicken dinners for $8 and steak dinners for $9. If 27 people spend $235, how many have chicken and steak? How can I write a linear eq      Log On


   

Question 696889: A large group goes to a restaurant and orders chicken dinners for $8 and steak dinners for $9. If 27 people spend $235, how many have chicken and steak? How can I write a linear equation for this problem?
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Let S = # of Steak dinners
Let C = Number of Chicken dinners
You would need to write two eqautions and see where they crossed.
Equation 1: S+%2B+C+=+27
Equation 2: 9S+%2B+8C+=+235
-------------------------------
Solve equation 1 for one of the variables
Equation 1: S+%2B+C+=+27
S+=+27+-+C
Now plug (27 - C) into equation 2 for S
Equation 2: 9S+%2B+8C+=+235
9%2A%2827+-+C%29+%2B+8C+=+235
Simplify
243+-+9C+%2B+8C+=+235
Combine like terms
243+-+C+=+235
Add C to both sides
243+=+235+%2B+C
Subtract 235 from both sides
highlight%288+=+C%29
Now plug 8 into equation 1 for C
Equation 1: S+%2B+C+=+27
S+%2B+%288%29+=+27
Subtract 8 from both sides
highlight_green%28S+=+19%29