WEBVTT
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We know that π¦ varies directly with π₯ and inversely with π§.
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Given that π¦ equals five when π₯ equals six and π§ equals three, find the value of π¦ when π₯ equals 24 and π§ equals 15.
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Weβre told that π¦ varies directly with π₯.
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So then we will have the equation π¦ equals ππ₯, where π is a constant.
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And we also know that π¦ varies inversely with π§.
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So we have the equation π¦ equals π divided by π§, where π is a constant.
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So how can we put these together to make one equation?
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Well, we can have π¦ equals π, and π needs to be multiplied by π₯ and divided by π§.
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So we have something like this.
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And we are given that when π¦ equals five and π₯ equals six and π§ equals three that weβre asked to find a value of π¦ when π₯ equals 24 and π§ equals 15.
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So in order to do that, we first must solve for π.
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So we simplify the right-hand side of the equation.
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Six divided by three is two.
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And now to solve for π, we must divide both sides of the equation by two.
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And five divided by two gives us that π is equal to 2.5.
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So we must replace π with 2.5 in our equation.
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So our equation is π¦ equals 2.5π₯ divided by π§.
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So we are supposed to find the value of π¦ when π₯ equals 24 and π§ equals 15.
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So we will replace π₯ with 24 and π§ with 15.
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So we need to take 2.5 times 24, which is 60, and 60 divided by 15 is four.
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Therefore, our final answer will be four.