Question

a fishing boat uses $14\frac{3}{4}$ gallons of fuel on a full - day fishing trip and $8\frac{1}{8}$ gallons of fuel on a half - day trip. find the total number of gallons of fuel used in 24 full - day trips and 16 half - day trips. the total amount of fuel used is \\(\square\\) gallons. (simplify your answer.)

Explanation:

Step1: Convert mixed numbers to fractions

$14\frac{3}{4} = \frac{14\times4 + 3}{4} = \frac{59}{4}$, $8\frac{1}{8} = \frac{8\times8 + 1}{8} = \frac{65}{8}$

Step2: Calculate fuel for full-day trips

$\frac{59}{4} \times 24 = 59 \times 6 = 354$

Step3: Calculate fuel for half-day trips

$\frac{65}{8} \times 16 = 65 \times 2 = 130$

Step4: Sum the two fuel amounts

$354 + 130 = 422$

Answer:

422