In Exercises 11–20, write an equation that expresses each relatio...

Question

In Exercises 11–20, write an equation that expresses each relationship. Then solve the equation for y.

x varies jointly as z and the sum of y and w.

Accepted Answer

Welcome back. I am so glad you're here. We are given this relationship, we're told that X varies jointly as Z. And the sum of Y and W. And X varies inversely as T. First. We are to write this as an expression. Alright, we recall from previous lessons on variation that the term that varies. So in this case X is going to go on the left hand side of the equal sign and then it is going to equal that constant term K. And now is it varies jointly. It's going to get multiplied by these terms here. It's going to get multiplied by Z. So cake time, Z. And times the sum of Y. And W. And we'll put that in parentheses to show that we do the sum first and then it gets multiplied by the constant K. Now for inverse variation inversely as T means that that T. Is going to go in the denominator below the constant term K. Alright, We have set up our expression but now we are to solve the equation for Y. Alright, let's start getting that Y by itself first. Let's multiply both sides by T. So the left will now read X. T. And the right hand side will read K. Z times parentheses, Y plus w. Those tees cancel out. Now let's divide both sides by Kz And on the right, the cases will cancel out and the left will read X. T divided by K. Z and it will equal Y plus W. We almost have that Y by itself. Let's subtract W from both sides. So on the right, the ws cancel out. And now we have Y equals. We have X. T divided by K, z minus W. We look at our answer choices and this matches with answer choice B. Well done. We'll catch you on the next one.

In Exercises 11–20, write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as z and the sum of y and w.

Key Concepts

Joint Variation

Formulating Equations

Solving for y

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