Gaussian elimination matrices word problem

Question

suppose you are organizing a dance. let A be the fixed cost (the cost before you include any people, example the rental of facility. and B the cost of the food snacks person. suppose you know the cost $1400 for 50 people and $2600 for 100 people.

A)set up system of two equations in terms a and b
B)use Gaussian elimination to solve for the fixed cost and cost per person
C)use the answer to find total cost for 160 people

Answer 1

a+50b=1400

a+100b=2600

 

solve for a

a=1400-50b

 

substitute into second equation

1400-50b+100b=2600

 

solve for b

50b=1200

b=24

 

solve for a

a+50(24)=1400

a=200

 

New equation

a+#people*b=cost

200+160*24=cost

200+3840=4040

Cost for 160 people =$4040