Question Video: Solving Proportion Equations to Find the Values of Unknowns | Nagwa Question Video: Solving Proportion Equations to Find the Values of Unknowns | Nagwa

# Question Video: Solving Proportion Equations to Find the Values of Unknowns Mathematics • Third Year of Preparatory School

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Given that π : π = 3 : 2 and π β π = 49, calculate the value of π.

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### Video Transcript

Given that π to π equals three to two and π minus π equals 49, calculate the value of π.

Weβre given information about the ratio of π to π alongside an equation that links π minus π with some constant. In order to use all of this to find the value of π, we will need to rewrite this equation so itβs purely in terms of π. So how do we do that?

Well, weβre going to use the fact that the ratio of π to π is equal to three to two. This will allow us to find a value of π divided by π. If the ratio of π to π is three to two, then when we divide π by π, weβre going to need to divide three by two. So π divided by π is equal to three over two.

Alternatively, we can find the reciprocal of both sides here. In other words, π over π is equal to two over three. Then, weβre 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. To do so, we multiply through by π. That gives us π equals two-thirds π.

We now replace π in the equation π minus π equals 49 with two-thirds π. So π minus two-thirds π is equal to 49. Well, one π is equivalent to three-thirds π. So we have three-thirds π minus two-thirds π, which is one-third π. So one-third π is equal to 49. To make π the subject, to solve for π, we divide through by one-third. And thatβs equivalent to multiplying by three. 49 times three is 147. So we found our value of π. π equals 147.

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