Question

1. a bowling alley charges $6.50 per game played and $4.00 for shoe rental. which table shows the cost, c, of renting shoes and playing g games of bowling?

a.
bowling cost

games, g	cost, c (dollars)
3	18.50
5	26.50

b.
bowling cost

games, g	cost, c (dollars)
3	23.50
5	36.50

c.
bowling cost

games, g	cost, c (dollars)
3	10.50
5	14.50

d.
bowling cost

games, g	cost, c (dollars)
3	19.50
5	32.50

Explanation:

Step1: Formulate the cost equation

The total cost \( c \) is the sum of the shoe rental (\$4.00) and the cost per game (\$6.50) times the number of games \( g \). So the equation is \( c = 4 + 6.5g \).

Step2: Test \( g = 1 \)

Substitute \( g = 1 \) into the equation: \( c = 4 + 6.5(1) = 10.5 \). So for 1 game, cost should be \$10.50.

Step3: Test \( g = 3 \)

Substitute \( g = 3 \): \( c = 4 + 6.5(3) = 4 + 19.5 = 23.5 \)? Wait, no, wait: \( 6.5\times3 = 19.5 \), plus 4 is 23.5? Wait, no, wait the first step: wait the shoe rental is \$4, per game \$6.50. So for \( g = 1 \): \( 4 + 6.5(1) = 10.5 \) (correct as in A and B). For \( g = 3 \): \( 4 + 6.5(3) = 4 + 19.5 = 23.5 \)? Wait no, wait 6.53 is 19.5, plus 4 is 23.5? But option A has 18.50 for \( g = 3 \). Wait, maybe I made a mistake. Wait, no: \( 6.5\times3 = 19.5 \), plus 4 is 23.5? Wait, no, 6.53 is 19.5, 19.5 + 4 is 23.5? But option B has 23.50 for \( g = 3 \). Wait, let's recalculate: 6.50 per game, so 3 games: 36.50 = 19.50, plus shoe rental 4.00: 19.50 + 4.00 = 23.50. Then for \( g = 5 \): 56.50 = 32.50, plus 4.00 = 36.50. So let's check the tables:

• Option A: \( g = 3 \), cost 18.50. 18.50 - 4 = 14.50, 14.50 / 3 ≈ 4.83, not 6.50. So A is wrong.
• Option B: \( g = 1 \): 10.50 (10.50 - 4 = 6.50, which is 6.50*1: correct). \( g = 3 \): 23.50 (23.50 - 4 = 19.50, 19.50 / 3 = 6.50: correct). \( g = 5 \): 36.50 (36.50 - 4 = 32.50, 32.50 / 5 = 6.50: correct).
• Option C: \( g = 1 \): 6.50 (no shoe rental? So wrong, because shoe rental is \$4, so cost should be at least \$4 + 6.50 = 10.50. So C is wrong.
• Option D: \( g = 1 \): 6.50 (same as C, wrong).

Wait, so the correct equation is \( c = 4 + 6.5g \). Let's verify each option:

• A: \( g = 1 \): 10.50 (correct). \( g = 3 \): 18.50. Let's see 18.50 - 4 = 14.50. 14.50 / 3 ≈ 4.83, not 6.50. So A is wrong.
• B: \( g = 1 \): 10.50 (10.50 - 4 = 6.50, 6.50*1: correct). \( g = 3 \): 23.50 (23.50 - 4 = 19.50, 19.50 / 3 = 6.50: correct). \( g = 5 \): 36.50 (36.50 - 4 = 32.50, 32.50 / 5 = 6.50: correct). So B matches the equation.

Wait, earlier I thought 6.5*3 +4 was 23.5, which is what B has. So B is correct.

Answer:

B. Bowling Cost (with Games, g: 1, Cost 10.50; 3, Cost 23.50; 5, Cost 36.50)