Question

The three scales below are perfectly balanced if $\cdot =3$ What is the value of $\Delta \text{and}\ast$?
Step: Find the value of ∆ and *​

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Answer 1

Step: Find the value of ∆ and *​
Let the value of $\Delta \text{and}\cdot$ be x and y respectively.
Given: $\cdot =3$

According to the problem,
Part (a) $\Rightarrow y+y+y+y+y=x+x+3+3$
$\Rightarrow 5y=2x+6$
$\Rightarrow 5y-2x=6$ ...(i)
Part (b) $\Rightarrow x+x=y+y+3+3$
$\Rightarrow 2x=2y+6$
$\Rightarrow 2x-2y=6$
$\Rightarrow x-y=3$
$\Rightarrow x=y+3$ ...(ii)

Substituting (ii) in equation (i),
$\Rightarrow 5y-2(y+3)=6$
$\Rightarrow 5y-2y-6=6$
$\Rightarrow 3y-6=6$
$\Rightarrow 3y=6+6=12$
$\Rightarrow y=\frac{12}{3}=4$ ...(iii)

Substituting (iii) in (ii),
$\Rightarrow x=4+3=7$
Hence, value of $\Delta =7$ and the value of $\ast =4$.