Question

a fishing boat uses $16\frac{1}{2}$ gallons of fuel on a full - day fishing trip and $9\frac{1}{4}$ gallons of fuel on a half - day trip. find the total number of gallons of fuel used in 22 full - day trips and 12 half - day trips.

the total amount of fuel used is \\(\square\\) gallons.
(simplify your answer.)

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(16\frac{1}{2}\) to an improper fraction. \(16\frac{1}{2}=\frac{16\times2 + 1}{2}=\frac{33}{2}\). Then, convert \(9\frac{1}{4}\) to an improper fraction: \(9\frac{1}{4}=\frac{9\times4+1}{4}=\frac{37}{4}\).

Step2: Calculate fuel for full - day trips

The number of full - day trips is 22, and each full - day trip uses \(\frac{33}{2}\) gallons. So the fuel used for full - day trips is \(22\times\frac{33}{2}\). We can simplify this: \(22\div2 = 11\), so \(11\times33=363\) gallons.

Step3: Calculate fuel for half - day trips

The number of half - day trips is 12, and each half - day trip uses \(\frac{37}{4}\) gallons. So the fuel used for half - day trips is \(12\times\frac{37}{4}\). We can simplify this: \(12\div4 = 3\), so \(3\times37 = 111\) gallons.

Step4: Calculate total fuel used

To find the total fuel used, we add the fuel used for full - day trips and half - day trips. So total fuel \(=363 + 111=474\) gallons.

Answer:

474