To find out how many miles per day Tina needs to bike to reach her goal, we can start by subtracting the miles she has already biked from her total goal:
500 miles - 75 miles = 425 miles left to bike
Next, we can divide the miles left to bike by the number of days she has left to complete the goal (15 days) to find out how many miles per day she needs to bike:
425 miles / 15 days = 28.33 miles per day (rounded to two decimal places)
Therefore, Tina needs to bike approximately 28.33 miles per day to reach her goal in 15 days.
To justify these steps using the property of equality, we can note that we are using the subtraction property of equality to subtract the miles Tina has already biked from her total goal, and then using the division property of equality to divide the miles left to bike by the number of days she has left. These properties allow us to perform the same operation on both sides of an equation while maintaining its equality.