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

Given that π‘Ž : 𝑏 = 3 : 2 and π‘Ž βˆ’ 𝑏 = 49, calculate the value of π‘Ž.

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Video Transcript

Given that π‘Ž to 𝑏 equals three to two and π‘Ž minus 𝑏 equals 49, calculate the value of π‘Ž.

We’re given information about the ratio of π‘Ž to 𝑏 alongside an equation that links π‘Ž minus 𝑏 with some constant. In order to use all of this to find the value of π‘Ž, we will need to rewrite this equation so it’s purely in terms of π‘Ž. So how do we do that?

Well, we’re going to use the fact that the ratio of π‘Ž to 𝑏 is equal to three to two. This will allow us to find a value of π‘Ž divided by 𝑏. If the ratio of π‘Ž to 𝑏 is three to two, then when we divide π‘Ž by 𝑏, we’re going to need to divide three by two. So π‘Ž divided by 𝑏 is equal to three over two.

Alternatively, we can find the reciprocal of both sides here. In other words, 𝑏 over π‘Ž is equal to two over three. Then, we’re going to make 𝑏 the subject because this will allow us to find an expression for 𝑏 in terms of π‘Ž that we can substitute into the equation. To do so, we multiply through by π‘Ž. That gives us 𝑏 equals two-thirds π‘Ž.

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

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