# Question Video: Solving an Equation Using the Equilibrium of Two Couples Mathematics

Fill in the blank: If the couples 𝐌₁ and 𝐌₂ are in equilibrium, where 𝐌₁ = 50𝐤, then 𝐌₁ − 𝐌₂ = ＿.

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### Video Transcript

Fill in the blank: If the couples 𝐌 sub one and 𝐌 sub two are in equilibrium, where 𝐌 sub one is equal to 50𝐤, then 𝐌 sub one minus 𝐌 sub two is equal to what.

The key point in this question is that the two couples 𝐌 sub one and 𝐌 sub two are in equilibrium. We know that if 𝐌 sub one and 𝐌 sub two are in equilibrium, then their magnitudes must be equal. We also know that they are opposites of one another, so 𝐌 sub one is equal to negative 𝐌 sub two, or 𝐌 sub one plus 𝐌 sub two must equal zero. This means that the two couples do not exert a net force on the body on which they act. In other words, the body itself is also in equilibrium.

We are told in the question that 𝐌 sub one is equal to 50𝐤. Substituting this into our second equation, we have 50𝐤 plus 𝐌 sub two is equal to zero. And subtracting 50𝐤 from both sides of this equation, we have 𝐌 sub two is equal to negative 50𝐤. We are now in a position to calculate 𝐌 sub one minus 𝐌 sub two. We have 50𝐤 minus negative 50𝐤. This is the same as 50𝐤 plus 50𝐤, which equals 100𝐤. We can therefore conclude that if the couples 𝐌 sub one and 𝐌 sub two are in equilibrium, where 𝐌 sub one is equal to 50𝐤, then 𝐌 sub one minus 𝐌 sub two is equal to 100𝐤.