Ratios, rates, and proportions — Basic example

- [Instructor] Seven pounds of plums make eight 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 seven pounds of plums for every eight 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 eight rolls to 20 rolls? How much larger is 20 than eight? Let's see, 20 divided by eight is 2 4/8, which is 2 1/2. So we multiplied by 2 1/2 or we have 2 1/2 times as many rolls when we go from eight to 20. So we're gonna need 2 1/2 times as many pounds to keep the ratios constant. So times 2.5, and what's seven times 2.5? Let's see, seven times two is 14. Seven times five is 3.5. 14 plus 3.5, this is going to be 17.5 pounds. Now, 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 more rolls than we're able to make with the seven 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. But if you're under time pressure, deductive reasoning isn't always a bad thing.