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? Choices: (A)3t = t + 4 (B)3t - 4 = t + 4 How many pairs of sunglasses did Ted have initially? ____ pairs

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?   Choices: (A)3t = t + 4 (B)3t - 4 = t + 4  How many pairs of sunglasses did Ted have initially?   ____ pairs

Bytelearn · Accepted Answer

Initial Denotation of Pairs: Let's denote the number of pairs Ted had initially as t. According to the problem, Edgar had three times as many pairs as Ted, so Edgar had 3t pairs. After giving four pairs to Ted, Edgar and Ted have the same number of pairs. This means that Edgar's new number of pairs (3t - 4) is equal to Ted's new number of pairs (t + 4). The equation representing this situation is: 3t - 4 = t + 4Equation Setup: To solve for t, we need to isolate the variable on one side of the equation. We can do this by subtracting t from both sides of the equation to get rid of the t on the right side. 3t - 4 - t = t + 4 - t This simplifies to: 2t - 4 = 4Isolating the Variable: Next, we add 4 to both sides of the equation to isolate the term with t on the left side. 2t - 4 + 4 = 4 + 4 This simplifies to: 2t = 8Solving for t: Finally, we divide both sides of the equation by 2 to solve for t. 2t / 2 = 8 / 2 This gives us: t = 4

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