Question

Here is a balanced hanger diagram. A circle weighs 3 grams, and a square weighs 2 grams. What is the weight of a triangle?

A: 11/3 grams
B: 7 grams
C: 3 grams

Answer 1

The weight of a triangle is 3 grams in the balanced hanger diagram. Thus, the correct answer is C: 3 grams.

Let's denote the weight of a triangle as T. The total weight on the right side is the sum of the weights of the triangles, circles, and squares, and on the left side, it's the sum of the weights of the circles and squares. We can set up an equation to represent the balance:

`\[ 2T + 2 * 3 + 5 * 2 = 1 * 3 + 5 * T + 2 * 2 \]`

Solving this equation will give us the weight of a triangle T:

2T + 6 + 10 = 3 + 5T + 4

Combine like terms:

2T + 16 = 5T + 7

Subtract 2T from both sides:

16 = 3T + 7

Subtract 7 from both sides:

9 = 3T

Divide by 3:

T = 3

So, the weight of a triangle is 3 grams.

Therefore, the correct answer is C: 3 grams.