Solve each problem. If y varies directly as x, and y=20 when x=4,...

Question

Solve each problem. If y varies directly as x, and y=20 when x=4, find y when x = -6.

Accepted Answer

Hey, everyone in this problem, we're asked to solve the following variation problem. If P varies directly as Q and P is equal to 80 or Q is equal to eight. Find P where Q is equal to we're given four answer choices. Option A 210. Option B 2.1, option C 10 and option D 640. Now we're told P varies directly as Q, hey, if P varies directly as Q, that means that P is proportional to Q. So we can write P is proportional to Q and we can replace that proportionality symbol with an equal sign as long as we include our variation constant. So P is proportional to Q. That means that P is equal to some constant K multiplied by Q. In this equation, P is equal to K multiplied by Q. We're gonna call equation one. Now we want to find P where Q is equal to 21. Now if we do that, if we try to substitute in our Q value, we don't know K yet. So we can't find our P value. So what we need to do first is use the other information given in the question to find K. Now we're given that when P is equal to 80 Q is equal to eight. OK. So let's substitute those values into our equation. One, we get that 80 is equal to K multiplied by eight. We can divide both sides by eight and we get that K is equal to 10. OK. So we found the K value for this equation. Now we can write our equation as P is equal to 10. Q. We're gonna call this equation two. OK. The exact same as equation one, we've just substituted in that known K value. Now, now that we know the K value, we can find the P value with that particular Q value we're interested in. So we wanna find P when Q is equal to 21. So let's substitute Q is equal to into equation two. When we do that, we get that P is equal to 10, multiplied by 21. And so P is equal to 210. And that is the P value when Q is equal to 21. That's what the question was asking us to find. So we found that the correct answer is 210 which corresponds with answer choice. A thanks everyone for watching. I hope this video helped see you in the next one.

Solve each problem. If y varies directly as x, and y=20 when x=4, find y when x = -6.

Key Concepts

Direct Variation

Finding the Constant of Variation

Substituting Values

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