Question

The cost to ship goods varies directly with the mass. Paul paid $20.40 to ship a package with mass 24 kg. Write an equation for this relationship.

a) C = 20.40 kg
b) C = 24 × 20.40
c) C = 20.40 × kg
d) C = 20.40 + 24

Answer 1

The equation for the relationship between the cost to ship goods and the mass is C = ($20.40/24)m.

Step-by-step explanation:

To write an equation for the relationship between the cost to ship goods and the mass, we need to use the concept of direct variation. In direct variation, the two quantities are related by a constant ratio.

Let's denote the cost to ship (C) and the mass (m). Since the cost varies directly with the mass, we can write the equation as:

C = km

Where k is the constant of variation.

In the given information, Paul paid $20.40 to ship a package with a mass of 24 kg. We can use this information to find the value of k. Plug in the values into the equation:

$20.40 = k(24)

Divide both sides by 24 to solve for k:

k = $20.40/24

So, the equation for the relationship is C = ($20.40/24)m. This represents that the cost to ship is $20.40 for every 1 kg of mass.