SOLUTION: Fundraising. The Buck Creek Fire Department served 250 dinners. A child’s plate cost $5.50 and an adult’s plate cost $9.00. A total of $1935 was collected. How many of each type of

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Fundraising. The Buck Creek Fire Department served 250 dinners. A child’s plate cost $5.50 and an adult’s plate cost $9.00. A total of $1935 was collected. How many of each type of      Log On


   

Question 1123330: Fundraising. The Buck Creek Fire Department served 250 dinners. A child’s plate cost $5.50 and an adult’s plate cost $9.00. A total of $1935 was collected. How many of each type of plate were served?
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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One approach is to solve the system of two equations in two unknowns


 C +    A =  250     dinners    (1)   (counting dinners;  C = # of child;  A = # of adults)
9C + 5.5A = 1935     dollars    (2)   ( counting dollars)


You can solve it using the Substitution method. For it, express C = 250-A  from eq(1) and then substitute into eq(2).
You will get

9*(250-A) + 5.5A = 1935.


Simplify and solve for C.  
When you find C, evaluate A = 250-C.


The rest is simple arithmetic, which I leave to you.



Another approach is to start directly from one single equation 

9*(250-A) + 5.5A = 1935.


It also has simple interpretation.


Again, simplify and solve for C.  
When you find C, evaluate A = 250-C.


The rest is simple arithmetic, which I leave to you.