Question

a fishing boat uses $15\frac{3}{8}$ 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 24 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

For the full - day trip fuel consumption: \(15\frac{3}{8}=\frac{15\times8 + 3}{8}=\frac{120+3}{8}=\frac{123}{8}\) gallons.
For the half - day trip fuel consumption: \(9\frac{1}{4}=\frac{9\times4+1}{4}=\frac{36 + 1}{4}=\frac{37}{4}\) gallons.

Step2: Calculate fuel for full - day trips

Number of full - day trips is 24. So fuel used for full - day trips is \(24\times\frac{123}{8}\).
We can simplify \(24\div8 = 3\), then \(3\times123=369\) gallons.

Step3: Calculate fuel for half - day trips

Number of half - day trips is 12. So fuel used for half - day trips is \(12\times\frac{37}{4}\).
We can simplify \(12\div4 = 3\), then \(3\times37 = 111\) gallons.

Step4: Calculate total fuel

Total fuel used is the sum of fuel used for full - day and half - day trips.
Total fuel=\(369+111 = 480\) gallons.

Answer:

480