If x is the number of days Ted is going to run, the given situation can be written in an algebraic way as follow:
12 + 3x = 48
12 because this is the number of miles Ted has already ran, 3x is the number of miles Ted has run after x days, and 48 because he wants to reach his goal of 48 miles.
In order to determine how many days he need to reach his goal, you solve the previous equation for x, just as follow:
12 + 3x = 48 subtract 12 both sides
3x = 48 - 12 simplify
3x = 36 divide by 3 both sides
x = 36/3
x = 12
Then, Ted needs 12 days to reach his goal of 48 miles