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Leo is baking a cake.
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In the first step of the recipe, he has to mix 200 milliliters of milk, 30 milliliters of treacle, and three beaten eggs together.
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One egg has a volume of 50 milliliters.
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The density of milk is 1.04 grams per milliliter.
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The density of treacle is 1.43 grams per milliliter.
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The density of beaten egg is 1.03 grams per milliliter.
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Calculate the density of the mixture.
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Give your answer to two decimal places.
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Now, in order to solve this problem, there’s actually a formula that we’re gonna use.
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And that formula is that density is equal to mass over volume.
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And we’re gonna use that formula because actually what we want to do is calculate the density of the whole mixture.
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A little tip here to help you answer this kind of question if you forget what the formula is, so density is equal to mass over volume.
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As if you look at the density, so for instance, we’ve got the density of milk is 1.04 and then it says grams per milliliter.
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Well, if you think about the units grams per milliliter, that’s grams, which is mass, divided by milliliter, which is volume.
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So that’s one way of actually reminding yourself of what the formula is.
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Okay, now, because we’re trying to find density, the first thing we’d look for is the total mass.
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So we’re gonna start off by actually finding the mass of each part.
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So we’re gonna start with the mass of the milk.
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And to actually find the mass of milk, we’re gonna rearrange our formula.
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And now, we’re gonna have that mass is equal to density multiplied by the volume.
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And we found that because actually we multiplied both sides of our equation by volume.
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So therefore, the mass of the milk is gonna be equal to 200 because it’s 200 milliliters multiplied by 1.04 because it’s 1.04 grams per milliliter, which gives us total mass of milk of 208 grams.
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And then, we’re gonna find the mass of the treacle.
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And this is 30 cause we have 30 milliliters of treacle multiplied by 1.43, again cause the density of treacle is 1.43 grams per milliliter.
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And this gives us a total mass of treacle of 42.9 grams.
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So now, we’ll move on to the mass of the egg.
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And the mass of the egg is equal to three multiplied by 50 and that’s because we got three eggs and each egg has a volume of 50 milliliters.
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And then, we get the result of this and multiply it by 1.03, which is the density of beaten egg, which gives us a total mass of egg of 154.5 grams.
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Okay, great, so now we found the mass of each individual part.
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We need to find the mass of the mixture.
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Well, the mass of the mixture is actually gonna be the masses of each part added together.
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So we’re gonna have 208 because that’s the mass of milk plus 42.9, the mass of treacle, plus 154.5, the mass of egg, which gives us the total mass of 405.4 grams.
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So now, what we need to do is actually find the volume because as we said density is equal to mass divided by volume.
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So let’s try and find the total volume of the mixture.
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Well, the total volume of the mixture is gonna be equal to 200 because that’s the volume of milk plus 30 the volume of treacle plus three multiplied by 50 and that’s because we have three beaten eggs each one of volume 50 milliliters.
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And this gives us a total volume of the mixture of 380 milliliters.
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So therefore, the total density of the mixture is gonna be equal to the total mass which is 405.4 divided by the total volume which is 380, which gives us an answer of 1.066842105263 et cetera.
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But have we finished?
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Is that the end of the question?
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No, not quite because we must always look and see how the question wants us to leave our answer.
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And it says leave your answer to two decimal places.
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And when we do that, we get a final answer of 1.07 grams per milliliter.
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And the way we got that final answer is because if we look at the answer we got, then in the second decimal place is a six — so we got 1.06 — and the number after is also a six.
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And because that number is five or greater, that means we actually round up the six that we had.
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So therefore, we get 1.07 grams per milliliter.