Video: GCSE Mathematics Foundation Tier Pack 3 • Paper 2 • Question 25

GCSE Mathematics Foundation Tier Pack 3 • Paper 2 • Question 25

02:44

Video Transcript

Tolu, Chris, and Mahmoud all sat an exam. There were 80 marks in total on the exam. Tolu got 77.5 percent of the marks. Chris got seventeen twentieths of the marks. Mahmoud got 65 out of 80. Who got the highest mark in the exam? You must show how you reached your answer.

We should begin by converting each of these into the same format. The easiest way to do so is to work out how many marks Tolu and Chris got since we already know that Mahmoud got 65 out of 80. We could alternatively convert each of these into percentages. But that is a slightly more complicated method.

We’re first told that Tolu got 77.5 percent of the marks. There were a total number of 80 marks available. So we need to work out 77.5 percent of 80. Remember when we’re performing a mathematical calculation, we can replace the word “of” with a multiplication sign. Many calculators also have a percentage button, which will allow you to type this calculation directly in.

However, if we remember that the word “percent” means out of 100, we can rewrite this calculation as shown. Typing 77.5 over 100 all multiplied by 80 gives us a value of 62. So Tolu got 62 marks.

Alternatively, we could have written 77.5 percent as a decimal. And we do that by dividing through by 100. 77.5 divided by 100 is 0.775. And when we type 0.775 multiplied by 80 into our calculator, once again, we get a value of 62.

We’re next told that Chris got seventeen twentieths of 80. We can once again replace “of” with the multiplication sign. And when we type in seventeen twentieths multiplied by 80, we get 68. So Chris got 68 marks.

An alternative way to perform this calculation would’ve been to work out the value of one twentieth first. We can work out the value of one twentieth of 80 by dividing 80 by 20. And that gives us four. When we know the value of one twentieth, we can work out the value of seventeen twentieths by multiplying this by 17. And 17 multiplied by four once again gives us 68.

Finally, we’re given that Mahmoud got 65 marks. 68 is larger than both 62 and 65. So Chris got the highest mark in the exam.

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