The cost c of printing a magazine is jointly proportional to the number of pages p in the magazine and the number of magazines printed m
Find the constant of proportionality if the printing cost is $50,312.5 for 3500 copies of a 115 page magazine k=?
To find the constant of proportionality, we need to set up a proportion using the given information.
The cost c is jointly proportional to the number of pages p and the number of magazines printed m, so we can write the equation as c = kp * m.
We are given that the printing cost is $50,312.5 for 3500 copies of a 115-page magazine.
Plugging in these values into the equation, we get: $50,312.5 = k * 115 * 3500.
Simplifying the equation, we get: $50,312.5 = 402500 * k.
To solve for k, divide both sides of the equation by 402500: k = $50,312.5 / 402500.
Now, divide the numerator and denominator by 125 to simplify the fraction: k = $403 / 3220.
Therefore, the constant of proportionality is approximately k = $0.125.
To find the constant of proportionality, we can use the formula for joint variation:
c = k * p * m
Given that the printing cost is $50,312.5 for 3500 copies of a 115-page magazine, we can substitute the values into the formula:
50312.5 = k * 115 * 3500
To find the value of k, we can solve for it:
k = 50312.5 / (115 * 3500)
k ≈ 0.12
Therefore, the constant of proportionality is approximately 0.12.