Question

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Answer 1

Answer:

3 gallons of diesel weight = 22.2 pounds

The constant of variation = 7.4

The quantities vary directly

Step-by-step explanation:

Given:

5 gallons of gas weights = 37 pounds

To find

a) the weight of 3 gallons of gas.

b) if the quantities vary directly or inversely.

c) the constant of variation.

Solution:

Applying unitary method to find weight of 3 gallons of gas.

If 5 gallons weight = 37 pounds

Then, 1 gallon will weight = $\frac{37}{5}$ =7.4 pounds

Thus, 3 gallons will weight = $3\times 7.4$ = 22.2 pounds

Listing out the data we have:

1 gallon = 7.4 pounds

3 gallons = 22.2 pounds

5 gallons = 37 pounds

From the data, we find out that as the number of gallons of gas increases the weight of gas also increases. This shows that these quantities are directly proportional to each other.

The unit rate of the quantities is called the constant of variation.

Unit rate: 7.4 pounds per gallon

Thus, the constant of variation = 7.4