Question

for a certain video game, the number of points awarded to the player is proportional to the amount of time the game is played. for every 2 minutes of play, the game awards 1 point. For every 9 minutes of play, the game awards 4 1/2 points. Find the constant of proportionality. Show every step of your work.

Answer 1

Let t = time in minutes and P = points. Since P is proportional to t, write
P = k t
where k is the constant of proportionality (points per minute).

Use the given data:

1) For t = 2, P = 1:
1 = k(2) → k = 1/2.

2) Check with t = 9, P = 4 1/2 = 4.5:
P = k t = (1/2)(9) = 4.5, which matches.

So the constant of proportionality is k = 1/2 point per minute (or 0.5 points per minute).