Question

A company makes 660 board games and a span of 4 hours and 1320 board games in a span of 8 hours what is the constant of proportionality

Answer 1

Constant of proportionality = 165 board games per hour

Step-by-step explanation

If the number of board games the company makes is y

And the number of hours it takes is x

If y varies directly as x, this can be written as

y ∝ x

Introducing the constant of proportionality, k, we have

y ∝ x

y = kx

We can then solve for k knowing that

when y = 660, x = 4 hours

OR when y = 1320, x = 8 hours

y = kx

660 = (k) (4)

660 = 4k

Divide both sides by 4

(660/4) = (4k/4)

165 = k

k = 165 board games per hour

Using the other conditions

y = kx

1320 = (k) (8)

1320 = 8k

Divide both sides by 8

(1320/8) = (8k/8)

165 = k

k = 165 board games per hour

Hope this Helps!!!