Video: GCSE Mathematics Foundation Tier Pack 3 • Paper 3 • Question 4

GCSE Mathematics Foundation Tier Pack 3 • Paper 3 • Question 4

06:12

Video Transcript

Rupert buys some footballs, tennis balls, ping pong balls, and cricket balls. He buys five footballs which weigh 430 grams each, 20 tennis balls which weigh 58.5 grams each, and 12 cricket balls which weigh 155.9 grams each. A ping pong ball weighs 2.7 grams. The total weight of all the balls is 5.2988 kilograms. Part a) How many ping pong balls did Rupert buy?

There is also a part b, which we’ll come on to later. Well, the first thing we want to do is we’re gonna have a look at the total weight of all the balls and that’s 5.2988 kilograms. Well, what you want to do with this is actually convert it to grams. And that’s because all the other measurements we have are in grams.

To help us do that, what we’ve got is the fact that one kilogram is equal to 1000 grams. So therefore, 5.2988 kilograms is gonna be equal to 5298.8 grams. And we got that by multiplying 5.2988 by 1000. Okay, so that’s the total weight of all of the balls. So what do we want to do next?

Well, next, what we want to do is actually work out the weight of the footballs, tennis balls, and cricket balls because then it’s actually the number of ping pong balls that Rupert bought that we’re trying to find.

Well, first of all, we’re gonna work out the weight of the footballs, which is gonna be five multiplied by 430. And that’s because he bought five footballs and they weigh 430 grams each. And this is gonna give us 2150 grams.

So next, it’s gonna be tennis balls we’ll work out. And that’s gonna be 20 multiplied by 58.5. That’s because 20 tennis balls were bought and they each weigh 58.5 grams.

And then, finally, it’s gonna be cricket balls. So we’ve got 12 cricket balls. Each weigh 155.9 grams each. So we’re gonna do 12 multiplied by 155.9, which is gonna give us 1870.8 grams, which is great. So we’ve now got the weight of the footballs, tennis balls, and cricket balls.

So now, what we need to do is actually find the total weight of all three types of balls. So therefore, to find the total weight, we’re gonna add these together, which is gonna give us a total of 5190.8 grams. So that’s the total weight for footballs, tennis balls, and cricket balls that Rupert bought.

Well, now, what we want to do is to actually find the total weight of the ping pong balls. And to enable us to do that, what we need to do is actually take the total weight of the footballs, cricket balls, and tennis balls away from the total weight of all of the balls that Rupert bought. So therefore, what we’re gonna have is 5298.8 minus 5190.8, which is gonna give us a total weight of ping pong balls of 108 grams.

Okay, so now, let’s move on to the final part of the question. Well, what the question is actually looking for is how many ping pong balls that Rupert bought. So to work this out, what we’re gonna do is actually divide the total weight of ping pong balls by the weight of one ping pong ball.

And it tells us that one ping pong ball weighs 2.7 grams. So therefore, as we said, the number of ping pong balls can be equal to 108 divided by 2.7, which will give us the answer of 40. So therefore, we can say that Rupert bought 40 ping pong balls.

Okay, great, that’s part a. Now, let’s move on to part b.

At a golf range, you can buy buckets of golf balls to a specified weight. Michelle orders 2.5 kilograms of golf balls. She estimates that a golf ball weighs about 40 grams. Part b) Part one) Using Michelle’s estimate, work out an approximation for the number of golf balls the Michelle should expect. Part two) If Michelle’s estimate is an underestimate, explain how this would affect your answer.

As we already explained in part a, we know that one kilogram is equal to 1000 grams. So therefore, we can say that the 2.5 kilograms of golf balls that Michelle orders is equal to 2500 grams. We got that by multiplying 2.5 by 1000. And the reason we’ve done that is because actually the weight of a golf ball that she estimates is in grams. So we want them both in the same unit.

So in order to get an estimate for the number of balls that Michelle should expect, what we’re gonna do is divide 2500 because that was the weight in grams of the balls that she ordered by 40. And that’s because that was the weight of one golf ball that she estimated.

Well, when we do this calculation, we get an answer of 62.5. But Michelle can’t get half a golf ball. So what we can say is that we can estimate that the number of golf balls that Michelle should expect is 63 golf balls and that’s because we’ve actually rounded 62.5 up.

So that’s great; that’s part b part one solved. Let’s move on to part b part two. In part b, what we need to do is work out whether if Michelle had an underestimate for her estimate, how would this affect the answer.

So if Michelle’s estimate was an underestimate, that means each of the golf balls would actually weigh more. If each of the golf balls weigh more, then, therefore, the number of golf balls would decrease. And this is because what we would have is 2500, which was our weight of the golf balls that she ordered, divided by a number greater than 40.

And therefore, as we’re gonna be dividing by a number greater than 40, then our result is in fact going to be a smaller number. So therefore, we can say that if the weight of each golf ball was greater, the number of balls would decrease. So therefore, that’s how Michelle’s estimate if it was an underestimate would affect the answer.

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