Video: AQA GCSE Mathematics Foundation Tier Pack 1 • Paper 1 • Question 15

Darius thinks of a number. 20% of Darius’s number is 124. 3% of Darius’s number is 18.6. Work out 49% of Darius’s number.

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Video Transcript

Darius thinks of a number. 20 percent of Darius’s number is 124. Three percent of Darius’s number is 18.6. Work out 49 percent of Darius’s number.

We’ve been asked to work out 49 percent of Darius’s number. But we don’t actually know what his number is. So how can we do this? Well, we need to use the other information we’ve been given, which is what 20 percent and three percent of Darius’s number are each equal to.

Let’s consider how we can make 49 percent using 20 percent and three percent. Well, 20 percent plus 20 percent, or two lots of 20 percent, will give us 40 percent. And three lots of three percent, or three percent plus three percent plus three percent, will give us nine percent. Adding these values together will then give us the 49 percent that we need.

So what we’re going to do then is work out 40 percent of Darius’s number, which we can do by doubling his value for 20 percent or just adding 124 to 124. We’ll then work out nine percent of his number by multiplying his value for three percent by three.

So 40 percent then, we add 124 to 124, which we can do using a column addition method. Starting from the right, four plus four is equal to eight, two plus two is equal to four, and one plus one is equal to two. So 40 percent of Darius’s number is 248.

For nine percent, we multiply 18.6 by three, which we can do using a column multiplication method. As only one of the numbers that we’re multiplying is a decimal, the decimal point in the answer will go directly below the decimal point in the question, so will go here.

Starting from the right then, three multiplied by six is equal to 18. So we put an eight and carry the one. Three multiplied by eight is equal to 24. And adding the one we’ve carried gives 25. So we put a five and carry the two. Three multiplied by one is three. And adding the two we’ve carried gives five. So we see that 18.6 multiplied by three is equal to 55.8.

Finally then, we need to add the two values we’ve just calculated using a column addition method. Remember, we need to line up the values in the correct column. And we can think of 248 as 248.0 if it helps. The decimal point in the answer will go directly below the decimal point in the question.

Adding from the right, zero plus eight is equal to eight. Eight plus five is equal to 13. Four plus five is equal to nine. And adding the one we’ve carried gives 10. Two plus nothing is equal to two. But adding the one we’ve carried gives three. So by scaling up the values we’ve been given for 20 percent and three percent of Darius’s number, we find that 49 percent of his number is 303.8.

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