Question

2)
there is a balance diagram. on the left side of the balance, there are 1 diamond (marked with a cross), 3 diamonds, and 1 trapezoid (marked with a cross) from top to bottom. on the right side of the balance, there are 1 diamond (marked with a cross), 2 circles, and 1 trapezoid (marked with a cross) from top to bottom.
given that circle = 3, trapezoid = 1, and we need to find the value of diamond (represented by a square box).

Explanation:

Step1: Analyze the balance

Let the value of $\diamondsuit$ be $x$. On the left side, we have $3$ diamonds and $1$ trapezoid, so the total weight is $3x + 1$. On the right side, we have $1$ diamond, $2$ circles, and $1$ trapezoid. The value of a circle is $3$ and trapezoid is $1$, so the total weight is $x + 2\times3 + 1 = x + 7$.

Step2: Set up the equation

Since the balance is equal, we set the two sides equal: $3x + 1 = x + 7$.

Step3: Solve for $x$

Subtract $x$ from both sides: $3x - x + 1 = 7$ $\implies$ $2x + 1 = 7$. Then subtract $1$ from both sides: $2x = 7 - 1$ $\implies$ $2x = 6$. Divide both sides by $2$: $x = \frac{6}{2} = 3$.

Answer:

$\diamondsuit = 3$