Final answer:
The correct equation to find the number of miles Gavin should bike on the first day to reach his 65-mile goal over four days, with each day biking 1.5 times as far as the day before, is x + 1.5x + 2.25x + 3.375x = 65, which is Option B. Option B is the correct equation: x + 1.5x + 2.25x + 3.375x = 65.
Step-by-step explanation:
To solve the problem regarding Gavin's goal to bike a total of 65 miles over four days with each day biking 1.5 times as far as the day before, we need to establish an equation based on the distance he bikes on the first day (x).
On the first day, Gavin bikes x miles. On the second day, he bikes 1.5 times as far, which can be written as 1.5x. On the third day, it's 1.5 times the distance of the second day, resulting in (1.5)^2x or 2.25x. Finally, on the fourth day, he bikes 1.5 times the distance of the third day, giving us (1.5)^3x or 3.375x.
Adding all these distances together to achieve the goal of 65 miles, we get the following equation:
x + 1.5x + (1.5)^2x + (1.5)^3x = 65
Simplified, that gives us:
x + 1.5x + 2.25x + 3.375x = 65
Option B is the correct equation: x + 1.5x + 2.25x + 3.375x = 65.