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Given that π to π equals three to two and π minus π equals 49, calculate the value of π.
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Weβre given information about the ratio of π to π alongside an equation that links π minus π with some constant.
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In order to use all of this to find the value of π, we will need to rewrite this equation so itβs purely in terms of π.
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So how do we do that?
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Well, weβre going to use the fact that the ratio of π to π is equal to three to two.
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This will allow us to find a value of π divided by π.
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If the ratio of π to π is three to two, then when we divide π by π, weβre going to need to divide three by two.
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So π divided by π is equal to three over two.
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Alternatively, we can find the reciprocal of both sides here.
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In other words, π over π is equal to two over three.
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Then, weβre going to make π the subject because this will allow us to find an expression for π in terms of π that we can substitute into the equation.
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To do so, we multiply through by π.
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That gives us π equals two-thirds π.
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We now replace π in the equation π minus π equals 49 with two-thirds π.
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So π minus two-thirds π is equal to 49.
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Well, one π is equivalent to three-thirds π.
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So we have three-thirds π minus two-thirds π, which is one-third π.
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So one-third π is equal to 49.
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To make π the subject, to solve for π, we divide through by one-third.
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And thatβs equivalent to multiplying by three.
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49 times three is 147.
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So we found our value of π.
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π equals 147.