Question

problem 3
create a balanced hanger using triangles that weigh 2 pounds and squares that weigh 3 pounds.

Explanation:

Step1: Understand the balance condition

For a hanger to be balanced, the total weight on the left side must equal the total weight on the right side. Let the number of triangles be \( t \) and the number of squares be \( s \). The weight of a triangle is 2 pounds and a square is 3 pounds. So the equation is \( 2t + 3s_{\text{left}}=2t + 3s_{\text{right}} \), but more simply, we can find a combination where the total weight on each side is equal. Let's find a common multiple of 2 and 3, like 6.

Step2: Find a valid combination

If we take 3 triangles on one side: \( 3\times2 = 6 \) pounds. On the other side, take 2 squares: \( 2\times3=6 \) pounds. So we can place 3 triangles on the left and 2 squares on the right (or vice versa, or other combinations like 6 triangles (12 pounds) and 4 squares (12 pounds), etc.). A simple one is 3 triangles (2 lb each) on one side and 2 squares (3 lb each) on the other.

Answer:

One possible balanced hanger: Place 3 triangles (each 2 pounds) on one side and 2 squares (each 3 pounds) on the other side (since \( 3\times2 = 2\times3 = 6 \) pounds, so the hanger will balance).