The price of gasoline purchased varies directly with the number of gallons of gas purchased. If 23 gallons are purchased for $37.90, what is the price of purchasing 20 gallons? Let x represent the number of gallons purchased, and let y represent the total price. Round your answer to two decimal places if necessary.

Answer: the price of purchasing 20 gallons is $32.96

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.

Let x represent the number of gallons purchased, and let y represent the total price.

Given that y varies directly with x, if we introduce a constant of proportionality, k, the expression becomes

y = kx

If y = $37.9 when x = 23 gallons, then

37.9 = 23k

k = 37.9/23

Therefore, the direct variation equation is

y = 37.9x/23

When x = 20 gallons, then

y = 37.9 * 20/23

y = $32.96