Question

problem 3: two different community centres organize end of year fairs for their communities.

they each charge an entrance fee and a cost per game. the information below shows how much fair a and fair b each charge if someone were to play a certain number of games.

fair a
\

$$\begin{array}{|c|c|} \\hline \\text{number of games played} & \\text{total cost (\\$)} \\\\ \\hline 4 & 53 \\\\ \\hline 6 & 54.50 \\\\ \\hline 8 & 56 \\\\ \\hline \\end{array}$$

fair b
graph showing points at (10, 36) and (20, 52)

a) determine an equation for the total cost (c) for each of the fairs, for a certain number of games played, n. show your work. (4 marks - 2 each)

fair a: \underline{\qquad\qquad\qquad\qquad} fair b: \underline{\qquad\qquad\qquad\qquad}

b) for how many games played will both fairs cost the same money? solve algebraically. (2 marks)

Explanation:

Find the linear equation for Fair A

$$
LATEXBLOCK0
$$

Find the linear equation for Fair B

$$
LATEXBLOCK1
$$

Solve for the intersection point algebraically

$$
LATEXBLOCK2
$$

Answer:

Question a

Fair A: \(C = 0.75n + 50\)

Fair B: \(C = 1.5n + 20\)

Question b

\(n = 40\) games