Video: Solving Word Problems Involving Ratios

The ratio of the areas of two plots of land, A and B, is 17 : 5. Given that the area of plot A is 60 m² larger than plot B, what is the area of plot B?

02:09

Video Transcript

The ratio of the areas of two plots of land, A and B, is 17 to five. Given that the area of plot A is 60 meters squared larger than plot B, what is the area of plot B?

So we have plot A and plot B. And the parts of our ratio that apply to each are the 17 applies to plot A. And the five applies to plot B. And that’s because we were told that the ratio of the area of the plots of lands A and B is 17 to five. So it’s in the order that it’s given.

Well, we’re also told that plot A is 60 meters squared larger than plot B. So therefore, we can say that 17 parts minus five parts is gonna be equal to 60. And that’s because we’re told that plot A is 60 meters squared larger than plot B. And plot A refers to 17 parts of our ratio. And plot B is five parts of our ratio. So therefore, we can say that 12 parts is equal to 60 meters squared. So therefore, if we want to find one part, we’re gonna divide each side by 12 because 12 divided by 12 is one. And when we do that, we get one part is equal to five.

So now, we need to see what the question is asking. And the question wants us to find the area of plot B. So how do we do that? We’ve got the area of one part. And we know that plot B has five parts of our ratio. So therefore, the area of B is gonna be equal to five, because that’s the number of parts that refer to plot B, multiplied by five. And that’s because five meters squared is what one part is worth. So this gives us the answer 25.

So we can say that if the ratio of the areas of two plots of land A and B is 17 to five, given that the area of plot A is 60 meters squared larger than plot B, the area of plot B is 25 meters squared.

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