# Video: Solving Proportion Equations Involving Direct Variation

If π¦ β π₯ and π₯ = 75 when π¦ = 25, find the value of π¦ when π₯ = 30.

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### Video Transcript

If π¦ varies directly or is proportional to π₯ and π₯ equals 75 when π¦ equals 25, find the value of π¦ when π₯ equals 30.

As π¦ and π₯ are proportional to each other, or as π¦ varies directly with π₯, as one of them increases, so does the other. In order to solve this question, we firstly need to find the constant of proportionality, which we will call the letter π. Weβll replace the proportion sign with equals π, giving us the equation π¦ equals π multiplied by π₯.

Our next step is to substitute in the values that weβre given in the question. We are told that when π₯ is 75, π¦ is 25. Therefore, 25 equals π multiplied by 75 or 75π. Balancing this equation by dividing both sides by 75 leaves us with 25 over 75 equals π. Simplifying this fraction gives us a final answer of π equals a third. The constant of proportionality is equal to a third.

In practical terms, this means that our value for π¦ is always a third of the value of π₯, or another way of saying this would be that π₯ is always three times π¦. To complete the question find the value of π¦ when π₯ equals 30, we now need to substitute the value of 30 into the equation π¦ equals one-third π₯. The calculation π¦ equals a third of 30 or a third multiplied by 30, therefore, when π₯ equal 30, π¦ equals 10.