Question Video: Combined Variation and Its Applications | Nagwa Question Video: Combined Variation and Its Applications | Nagwa

# Question Video: Combined Variation and Its Applications

We know that π¦ varies directly with π₯ and inversely with π§. Given that π¦ = 5 when π₯ = 6 and π§ = 3, find the value of π¦ when π₯ = 24 and π§ = 15.

01:44

### Video Transcript

We know that π¦ varies directly with π₯ and inversely with π§. 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.

Weβre told that π¦ varies directly with π₯. So then we will have the equation π¦ equals ππ₯, where π is a constant. And we also know that π¦ varies inversely with π§. So we have the equation π¦ equals π divided by π§, where π is a constant. So how can we put these together to make one equation?

Well, we can have π¦ equals π, and π needs to be multiplied by π₯ and divided by π§. So we have something like this. And we are given that when π¦ equals five and π₯ equals six and π§ equals three that weβre asked to find a value of π¦ when π₯ equals 24 and π§ equals 15.

So in order to do that, we first must solve for π. So we simplify the right-hand side of the equation. Six divided by three is two. And now to solve for π, we must divide both sides of the equation by two. And five divided by two gives us that π is equal to 2.5. So we must replace π with 2.5 in our equation.

So our equation is π¦ equals 2.5π₯ divided by π§. So we are supposed to find the value of π¦ when π₯ equals 24 and π§ equals 15. So we will replace π₯ with 24 and π§ with 15. So we need to take 2.5 times 24, which is 60, and 60 divided by 15 is four. Therefore, our final answer will be four.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions