Question

5 gallons of diesel weighs 37 pounds. How much does 3 gallons of diesel weigh? Do these quantities (volume and weight) vary directly or inversely? Find the constant of variation.

Answer 1

Answer:

22.2 pounds and 1g = 7.4p

Step-by-step explanation:

Lets go in an inverse sense, finding firstly the constant variation and then the weight of 3 gallons.

The constant variation is the relation between gallons of diesel volume and pounds of diesel weight. For thise we would like to find how many pounds of diesel weights 1 gallon. We have the following equality:

5 gallons = 37 pounds

Now, lets divide both sided by 5, as we know the equality will still:

5/5 gallon = 37/ 5 pounds

1 gallon = 7.4 pounds

So, this is the constant variations: every extra gallons weights 7.4 pounds. We could also do this in terms of pounds, which means, parting from:

5 gallons = 37 pounds

Divide both sides by 37:

5/37 gallons = 1 pound

0.081 gallons = 1 pound

Every extra pound means 0.081 more gallons.

Now, as we want the weight of 3 gallons we can use our first relation and multiplying by 3:

1 gallon = 7.4 pounds

3 gallons = 22.2 pounds