Video: GCSE Mathematics Foundation Tier Pack 2 • Paper 2 • Question 12

GCSE Mathematics Foundation Tier Pack 2 • Paper 2 • Question 12

02:23

Video Transcript

To raise money, Emily and Michael take part in timed events. Emily makes and sells as many cupcakes as she can in an hour. She makes 16 cupcakes and sells each of them for 55 p. Michael completes a sponsored silence and manages to be silent for eight hours. In total, he raises 70 pounds and 50 pence. Show that Michael raises more money per hour than Emily.

First, let’s go through and highlight the relevant information. Emily makes cupcakes for an hour. She makes 16 cupcakes and sells them each for 55 p. Michael spends eight hours being silent. And in total, he raises 70 pounds and 50 pence.

Now, we need to label our working out very clearly. So, first of all, we’re talking about Emily. She makes 16 cupcakes in one hour. And because she sells them each for 55 p, that’s 16 times 55, which when we put into our calculator gives us 880 pence. So the rate of raising money that Emily achieves is 880 pence per hour.

Michael, on the other hand, raises 70 pounds and 50 pence. But it takes him eight hours. But we want to know his earning rate per hour. So eight hours divided by eight gives us one hour. But if we’ve only got an eighth of the amount of time, he’s going to earn an eighth of the amount of money.

So we have to divide 70.50 by eight. And that gives us 8.8125. Well, that’s eight pound 81 and a quarter per hour. Obviously, we can’t raise quarter of a pence. So we’re gonna round to the nearest penny, so eight pound 81 per hour.

Now, we’ve got a slight problem. We’ve got Michael’s earning rate in pounds per hour and Emily’s earning rate in pence per hour. We need to either convert pence to pounds or pounds to pence. And it doesn’t matter which one you do, so long as you remember that there are 100 pence in a pound. In my case, I’m gonna convert Emily’s pence into pounds. 880 divided by 100 is 8.80. So Emily earns eight pound and 80 per hour.

And finally, we just need to make a comparison of the two. Eight pound 81 is greater than 8 pounds 80. So Michael earns more than Emily. In fact, he earns one p an hour more.

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