Solve each problem. If m varies jointly as x and y, and m=10 when...

Question

Solve each problem. If m varies jointly as x and y, and m=10 when x=2 and y=14, find m when x=21 and y=8.

Accepted Answer

Hey, everyone in this problem, we're asked to solve the following variation problem. If P varies jointly as Q and R find P where Q is equal to four and R is equal to 16. The value of P is 40 where Q is equal to two and R is equal to 10. We're given four answer choices. Option A 64 option B 32 option C 128 and option D 256. Now we're told P varies jointly as Q and R. What that means is that P is proportional to Q and proportional to R at the same time. And so P is going to be proportional to the product Q multiplied by R. Now, we have this proportional symbol, we can replace that with an equal sign. But when we do that, we have to add in our variation constant. So we have that P is equal to K multiplied by Q multiplied by R or K is our constant. Now, we don't know the value of K yet. So we aren't able to find P with our given Q and R V. OK. So we need to find K first and we can use the other information we're given in order to do. So we're gonna call this equation one. And that's the equation P is equal to K multiplied by Q multiplied by R. We're told in the problem that P is equal to 40 when Q is equal to two, an R is equal to 10. So we're gonna substitute those three values into our equation one. And then the only unknown in that equation will be K and we can solve for K value. So we get 40 is equal to K multiplied by two, multiplied by 10. OK. That means that 40 is equal to 20 K, we can divide both sides by 20 and we get that K is equal to two. So now we have K is equal to two that tell the center equation is actually P is equal to two multiplied by Q multiplied by R. And we're gonna call this equation two. Now this is the same equation one. We've just substituted in that K value that we know. Now. Now we have our K value, we can find P using the Q in our values that we're interested in. So we're gonna substitute Q is equal to four and R is equal to 16 into this second equation. The equation with a K value we're gonna have that P is equal to two multiplied by four multiplied by 16, which gives us a P value of 128. OK. So we were able to find P when we have Q is equal to four and R is equal to 16, which is what the question was asking us to do. We found that the correct answer is 128 which corresponds with answer choice. C thanks everyone for watching. I hope this video helped see you in the next one.

Solve each problem. If m varies jointly as x and y, and m=10 when x=2 and y=14, find m when x=21 and y=8.

Key Concepts

Joint Variation

Finding the Constant of Variation

Substitution in Equations

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