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I now want to re-figure out what this mystery mass is,

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but we're going to start using a little bit more of mathematics.

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And mathematics really are just a language of symbols for representing ideas --

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for representing relationships between things.

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And so the first thing I want you to do is think about if you can express a relationship mathematically

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between this side of the scale and that side of the scale.

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And I'll give you some hints:

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we know that they have equal mass, so maybe you set some type of relationship using an equal sign --

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somehow showing that this right over here is equal to that and I'll give you a few seconds to do that.

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So let's think about it a little bit. What do we have on this side?

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Well, we have our mystery mass,

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and I'll represent that mystery mass by the question mark - right over here.

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But that's not the only thing we have on the left hand side: we also have these other three kilograms.

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So let me write over here, I'll just add, we'll assume that we're dealing with kilograms.

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So we have the mystery mass in kg plus three more kg. That's what we have here on the left hand side.

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Now what do we have here on the right hand side. Well just have 1,2,3,4,5,6,7,8,9,10 kg.

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So we just have 10 on the right hand side.

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And what else do we know?

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Well, we know that the scale is balanced --

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that the mass here is equal to the mass here, because the scale is balanced, the way it's been drawn.

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We know that these two things are equal.

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So we have just set up an equation. We're using question mark as our unknown.

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We don't know what this mystery mass is.

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If we add 3 kg to it, then we see that it has the exact same mass as 10 kg.

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Now my question to you is, what can we do to this equation

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so that we can essentially solve for the unknown,

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so that we can figure out what the unknown is.

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Well we saw in the last little problem that we had

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that if we wanted to figure out this mystery mass

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we had to remove, 3 of these, 3 kg from both sides.

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If we just removed 3 kg from one side

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then the scale wouldn't be balanced any more.

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And we really wouldn't be able to say that the mystery mass

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is equal to the thing on the right.

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In order to say they're equal this stuff actually has to actually be balanced.

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So in the last video, we removed three of these, we removed three kg from both sides

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in order to keep the scale balanced.

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So mathematically we'll do the exact same thing over here.

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We will remove 3 not from side --

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if we remove three from one side then it wouldn't be equal anymore --

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we need to remove three from both sides.

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So we need to remove three, we need subtract three,

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from both sides of the equation in order to keep the scale balanced.

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So on the left hand side, what are we left with?

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Well, just like over here, we're left with just the question mark.

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Three minus three is zero.

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So on the left hand side we're left with just the question mark.

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And on the right hand side, we're left with ten minus three which is seven.

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10 - 3 which is 7.

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And we get the exact same result: question mark is equal to seven.

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And if we're doing it in kg then this is seven kg.