Practice Question: Solving for X – Ratio and Proportion (Nursing)

00:00 Okay. So, let's try some other examples. 6:10, is it equal 18 to what? So for 6:10, what will it take for 18 to be equal to x, the unknown number? Well, let's walk through. We know 6:10 equals 18:x, that's how it's written.

00:21 Then the second step, we do the cross multiplication, right? So we've got it in the fraction format, 6/10. The numerator is the top number.

00:30 The denominator is the bottom number. So, we always put 6/10, 18/x.

00:36 Then we do the cross multiplication. We come up with 6x equals 180.

00:43 Now we know in order to -- we gotta get x by itself, right? X needs to be all by itself so how we do that is by dividing each side of the equation by the number that's in front of the x.

00:55 Since 6 is in front of the x, we divide both sides by 6.

01:01 So 6x divided by 6 equals 1 and then 180 divided by 6 equals 30.

01:10 Now we come up with x by itself because we divided by 6. That gives us 1x.

01:16 We can just write it as x equals 30. So x is the remaining number.

01:22 Now remember you go back and check your work.

01:25 So plug 30 in instead of x. 6 times 30 equals 10 times 18.

01:33 Yes. We've got a great ratio there. It's equal and proportionate. Good job.

01:39 Let's try a second example. Now, if you want, it might be a good time to pause the video, work the problem by yourself or you can choose to walk through it with us right now.

01:49 You choose what's best for you. So we multiply the extremes, then the means.

01:54 We place the x on the left side of the equation then you wanna divide each side of the equation by the number in front of the x which is 3.

02:03 That leaves x equals 32. X divided by 3 equals 1x or just x. 96 divided by 3 equals 32.

02:14 So you go back, you check your work.

02:17 You plug back in the value of x to the original formula and it works out.

02:23 3 times 32 is 96. 8 times 12 is 96. We got the right dosage.

02:28 Okay, so remember. When 3 of the 4 numbers of a ratio are known, x can be used as a placeholder.

02:36 That will help us figure what that fourth number is.

02:39 And in clinical practice, that fourth number is the medication dosage as ordered by the physician.

02:45 So you identify the known ratio and the unknown ratio.

02:50 You set up the proportion, just like we've already done.

02:54 You cross multiply and solve, just like we've already done and then you check the answer by plugging in the result into the unknown ratio and it should all line up. Okay. Really, I promise that's as straightforward as it is.

03:10 Thank you for watching our video today.