Berto has $12 to put gas in his car. If gas costs $3.75 per gallon, which ordered pair relating number of gallons of gas, x, to the total cost of the gas, y, includes the greatest amount of gas Berto can buy?

Answer 1

To determine the maximum number of gallons of gas Berto can buy with $12, we need to set up the relationship between the number of gallons of gas, \( x \), and the total cost of the gas, \( y \). We know the price of gas is $3.75 per gallon.

First, write the equation that relates the total cost \( y \) to the number of gallons \( x \):
\[ y = 3.75x \]

Berto has $12 to spend on gas (i.e., \( y \leq 12 \)). We need to find the maximum \( x \) that satisfies this condition.

Substitute \( y = 12 \) into the equation to find the maximum \( x \):
\[ 12 = 3.75x \]

Solve for \( x \):
\[
x = \frac{12}{3.75}
\]

Calculate the division:
\[
x = \frac{12}{3.75} = 3.2
\]

So, the maximum number of gallons Berto can buy is 3.2 gallons.

The ordered pair representing the relationship between the number of gallons of gas and the total cost for this maximum amount is:
\[
(3.2, 12)
\]

Therefore, the ordered pair \((x, y)\) that includes the greatest amount of gas Berto can buy is:
\((3.2, 12)\)