Math question for Helena

Question

A bowling alley charges customers a fee for every game bowled plus an initial fee for shoe rental. The total cost, y, depending on the number of games bowled, x, is shown in the table.

Games	Cost ($)
4	13.00
7	20.50
8	23.00
10	28.00

The cost increases by $ for each game bowled.

The initial fee for a shoe rental is $.

The cost increases by $ for every 6 games bowled.

Answer 1

From the table, 4 games cost $13.00 = S + 4G, where S = cost of shoe rental and G = number of games played.

Notice that 8 games cost $23.00. Eight games is double 4 games, but the cost is not double that of 4 games.

Set up simultaneous equations (1) and (2) to show what is going on

(1) $13 = S + 4G

(2) $23 = S + 8G

Multiply all terms in (1) by -1 and add to (2)

(2) $23 = S + 8G

(-1) -$13 =-S - 4G

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$10 = 4G

Divide both sides by 4 to see that G, the price of each game = $2.50

Plug $2.50 for G into either (1) or (2) and solve for S = $3.00, the price of shoe rental.

For every 6 games, the price increases by 6*$2.50 = $15.00