Use the four-step procedure for solving variation problems given ...

Question

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10.

y varies inversely as x. y = 12 when x = 5. Find y when x = 2.

Accepted Answer

Welcome back. I am so glad you're here. We are given this variation problem. We are told that why varies inversely as X. When we have variation, the variable that varies. So in this case the Y goes on the left hand side of the equal sign. And because it varies, it equals the constant term. And now when it varies inversely, that means K is being divided by the term that varies inversely. So in this case K divided by X. We've set up our equation and now we're given some more information. We're told that Y equals 13 and that X equals where X equals seven. So we can say replacing Y with 13. So 13 equals the constant term K divided by X equals seven. So replacing X with seven. So we have an equation there, we are asked to find Y where X equals three. So we want to solve for Y where X equals three. Okay, well in order to solve for why in that equation we need to know what the constant term K is and we can solve for that in this equation here because the only term missing is K. So let's multiply both sides by seven to cancel out the sevens on the right hand side and times seven is 91. So we have 91 equals K. We can replace the K. Over here on the right with a 91 And why equals 91 divided by three. That's actually as simplified as that one is going to get. So we look at our answer choices and that matches with answer choice. C. Well done, we'll catch you on the next one.

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies inversely as x. y = 12 when x = 5. Find y when x = 2.

Key Concepts

Inverse Variation

Constant of Variation

Four-Step Problem-Solving Procedure

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