Final answer:
The equation to find the initial number of pairs of sunglasses Ted had is 3t - 4 = t + 4, where t represents Ted's initial number of pairs.
Step-by-step explanation:
To find the equation that represents this situation, we can use the variable t to represent the initial number of pairs of sunglasses Ted had. We are told that Edgar had three times as many pairs of sunglasses as Ted, which can be represented as 3t. After giving four pairs to Ted, Edgar has 3t - 4 pairs, and Ted has t + 4 pairs. It's stated that now they have the same number of pairs, so we can set these two expressions equal to each other to form the equation:
3t - 4 = t + 4
This equation can then be solved to find the value of t, the initial number of pairs Ted had.