Question

Edgar had three times as many pairs of sunglasses as his friend Ted. Since Edgar didn't wear all of them regularly, he gave four pairs to Ted. Now they have the same number of pairs.
Which equation can you use to find t, the number of pairs Ted had initially?
How many pairs of sunglasses did Ted have initially?
pairs

Answer 1

Let \( t \) be the number of pairs of sunglasses Ted had initially. Since Edgar had three times as many pairs of sunglasses as Ted, we can express the number of pairs Edgar had as \( 3t \).

After Edgar gives 4 pairs of sunglasses to Ted, we need to set up the equation based on the new quantities:

- Edgar's new number of pairs: \( 3t - 4 \)
- Ted's new number of pairs: \( t + 4 \)

According to the problem, after the transfer, they have the same number of pairs of sunglasses:

\[
3t - 4 = t + 4
\]

To solve for \( t \):

1. Subtract \( t \) from both sides:
\[
3t - t - 4 = 4
\]
Simplifying gives:
\[
2t - 4 = 4
\]

2. Add 4 to both sides:
\[
2t = 8
\]

3. Divide both sides by 2:
\[
t = 4
\]

Therefore, Ted initially had \( \boxed{4} \) pairs of sunglasses.