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Ratios, rates, and proportions — Basic example

Video transcript
- [Voiceover] 7 pounds of plums make 8 rolls of fruit leather. If every batch of fruit leather requires the same amount of plums, how many pounds of plums are required to make 20 rolls of fruit leather? So, let's set up a ratio. We need 7 pounds of plums for every 8 rolls, 8 rolls of fruit leather. Now, we need to think about how many pounds of plums we're gonna need. How many pounds of plums we're gonna need to make 20 rolls of fruit leather. 20 rolls of fruit leather. Well, let's see. What have we done? To go from 8 rolls to 20 rolls, how many times do we have to, how much larger is 20 than 8? Let's see, 20 divided by 8 is 2 and four-eighths, which is 2 and a half. So, we multiplied by 2 and a half, or we have 2 and a half times as many rolls when we go from 8 to 20. So we're going to need 2 and a half times as many pounds to keep the ratios constant. So, times 2.5, and what's 7 times 2.5? Well, let's see. 7 times 2 is 14. 7 times 5 is 3.5. 14 plus 3.5, this is going to be, this is going to be 17.5 pounds. And that's this choice right over here. And actually, even looking at the choices, you might have been able to get here even without doing this. Not too intensive mathematics. Because you can say, okay look, the pounds are kind of close to the amount of leather. But they're less than it. So, we wouldn't want 23 pounds of plums if we make 20 rolls of fruit leather. This is more than 20. And if we're making, if we're making more rolls than the 7 pounds, than we were able to make with the 7 pounds, we're not gonna be able to have fewer pounds there. So you could have actually ruled out all of them just based on the logic to get to 17.5. But it's always satisfying to do it the right way. All right, but if you're under time pressure, you know, deductive reasoning isn't always a bad thing.