Question

the image shows a balance scale. on the left side, there are 5 hexagons (one of which is crossed out) and 1 triangle (crossed out). on the right side, there are 2 diamonds (each labeled 5) and 1 triangle (crossed out). below the image, its given that the triangle (△) = 1 and the diamond (◇) = 5. we need to find the value of the hexagon (hexagon symbol).

Explanation:

Step1: Analyze the left side

Left side has 5 hexagons (let's call hexagon value \( h \)) and 1 triangle (value 1, crossed out, so we subtract it? Wait, no, the balance: left total should equal right total. Wait, left: 5 hexagons + 1 triangle (but triangle is crossed, maybe left has 5h + 1 (but crossed, so maybe left is 5h - 1? No, right side: 2 diamonds (each 5) + 1 triangle (1, crossed). So right side: 25 + 1 (but crossed, so 25 - 1? Wait, maybe the crossed items are removed. So left: 5h (since 1 triangle is crossed, so left has 5h). Right: 25 (since 1 triangle is crossed, so right has 25). Wait, no, let's re-express.

Wait, the balance: left side has 5 hexagons and 1 triangle (but triangle is crossed, so maybe the left total is 5h + 1 (but the triangle is removed, so 5h - 1? No, maybe the crossed items are not part of the balance. Wait, the diagram: left string has 5 hexagons and 1 triangle (crossed), right string has 2 diamonds (each 5) and 1 triangle (crossed). So the balance is: 5h + 1 (triangle) - 1 (crossed triangle) = 25 + 1 (triangle) - 1 (crossed triangle). Simplify: 5h = 25. So 5h = 10. Then h = 10 / 5 = 2. Wait, no, maybe the crossed items are subtracted. Wait, left: 5 hexagons + 1 triangle (value 1) but the triangle is crossed, so left total is 5h + 1 - 1 = 5h. Right: 2 diamonds (each 5) + 1 triangle (value 1) but the triangle is crossed, so right total is 2*5 + 1 - 1 = 10. So 5h = 10, so h = 2.

Step2: Solve for hexagon

We have 5h = 2*5 (since right side is 2 diamonds, each 5, and the crossed triangle cancels with left's crossed triangle). So 5h = 10. Then h = 10 / 5 = 2.

Answer:

2