If 15 gallons of gasoline cost $45.00, how many gallons of gasoline cost $24.00?
$\frac{45}{15}=\frac{24}{x}$
We are given that 15 gallons of gasoline cost \(\$45.00\). We want to determine the number of gallons, represented by \(x\), that can be purchased for \(\$24.00\). The relationship between the quantity of gasoline and its cost is directly proportional, meaning the cost per gallon remains constant. We are provided with the equation \(\frac{45}{15} = \frac{24}{x}\) to model this relationship.
First, we calculate the cost per gallon (unit price) by dividing the total cost by the number of gallons: \[\frac{45}{15} = 3.\] This indicates that gasoline costs \(\$3.00\) per gallon.
Given that the cost per gallon is \(\$3.00\), we set up the proportional relationship where the cost of \(x\) gallons is \(\$24.00\): \[3 \times x = 24.\] To solve for \(x\), we divide both sides of the equation by 3: \[x = \frac{24}{3} = 8.\] Therefore, \(8\) gallons of gasoline can be purchased for \(\$24.00\).
Understanding unit prices is a fundamental skill for everyday budgeting. For instance, if you are grocery shopping and see different package sizes for the same item, you can use the same proportionality method to calculate the cost per unit (like price per ounce) to determine which package offers the better value. This simple math helps you make informed financial decisions while shopping.