A van travels 180 miles on 12 gallons of gas. At that rate, how much gas will it need to travel 330 mile

To find out how much gas the van will need to travel 330 miles at the same rate, we can use the concept of proportionality. Given: - Distance traveled = 180 miles - Gas consumed = 12 gallons We can set up a proportion to find the gas needed to travel 330 miles: \[ \frac{180 \text{ miles}}{12 \text{ gallons}} = \frac{330 \text{ miles}}{x \text{ gallons}} \] Where \( x \) is the amount of gas needed to travel 330 miles. Now, we can solve for \( x \) by cross-multiplying and simplifying the equation. Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{180}{12}=\frac{330}{x}\) - step1: Find the domain: \(\frac{180}{12}=\frac{330}{x},x\neq 0\) - step2: Divide the terms: \(15=\frac{330}{x}\) - step3: Swap the sides: \(\frac{330}{x}=15\) - step4: Cross multiply: \(330=x\times 15\) - step5: Simplify the equation: \(330=15x\) - step6: Rewrite the expression: \(15\times 22=15x\) - step7: Evaluate: \(22=x\) - step8: Swap the sides: \(x=22\) - step9: Check if the solution is in the defined range: \(x=22,x\neq 0\) - step10: Find the intersection: \(x=22\) The van will need 22 gallons of gas to travel 330 miles at the same rate.