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 directly as z and inversely as the sum of y and w.

Accepted Answer

Welcome back. I am so glad you're here. We are given this relationship, we are told that X varies directly as P and the difference of Y and Z. Where Y is greater than Z, and that X varies inversely as the sum of T and w. Well we have a variation problem. So we're going to start off by writing that as the variable that varies. So X on the left hand side of an equal sign and it varies, so X equals K, the constant term. And now when it varies directly, K gets multiplied by any terms that vary directly. So K will be multiplied by P and by the difference of Y and Z. So we'll put this in parentheses and we'll take why minus the inside parentheses to show that we find that difference first, and then that gets multiplied by the constant term K. Well, X also varies inversely as the sum of T and W. And when there's inverse variation, then K is being divided by whatever variables are being inversely varied. So in this case it's going to be the sum of T and w. So we'll put parentheses again and we'll put T plus W in parentheses to show that that some happens first and then it will be K divided by that some great. We have set up the expression and now we are asked to solve the equation for P. So we want to get P by itself. Let's start off by multiplying both sides by T plus W and that will clear out the denominator on the right hand side. So on the left we'll have X times T plus W. And that will equal K times p times parentheses Y minus Z. Now we can divide both sides by everything that's not the P. Over here all these factors we can divide by K and by parentheses Y minus Z. This will cancel out the case and cancel out the y minus Z. S. And what we do to one side, we do to the other K times y minus Z. And then on the right hand side it's just P. By itself. So I'll write P equals which is exactly what we were solving for. And then the numerator is X times parentheses T plus W. And the denominator is K times parentheses y minus Z. 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 directly as z and inversely as the sum of y and w.

Key Concepts

Direct Variation

Inverse Variation

Combining Direct and Inverse Variation

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