Video: GCSE Mathematics Foundation Tier Pack 5 • Paper 1 • Question 25

GCSE Mathematics Foundation Tier Pack 5 • Paper 1 • Question 25

04:08

Video Transcript

There are 600 passengers on a plane. Seven thirtieths of the passengers have blue eyes. 60 percent of the passengers have brown eyes. The rest of the passengers have green eyes. Calculate the number of passengers on the plane who have green eyes.

In order to calculate the number of passengers on the plane who have green eyes, we must first calculate the number of passengers on the plane who have blue eyes and brown eyes. We’re told that seven thirtieths of the passengers have blue eyes, so we need to calculate seven thirtieths of 600.

There are a number of different ways that we could do this. For example, we could remember that, in a question involving fractions, the word “of” means “multiply.” So seven thirtieths of 600 means seven thirtieths multiplied by 600. We could work this out as a fraction calculation by writing 600 as 600 over one. And then we could simplify by cross-cancelling. 30 divided by 30 is one, and 600 divided by 30 is 20. So we could simplify to seven over one multiplied by 20 over one.

To multiply fractions, we multiply the numerators together and multiply the denominators. So seven multiplied by 20 is 140, and one multiplied by one is one. We have the fraction 140 over one, which is just equal to 140.

Another method of finding seven thirtieths of a number, which may be more straightforward, is to first find one thirtieth of that number by dividing by 30 and then multiply it by seven. 600 divided by 30 is 20. We can see this because 600 divided by 30 means 600 over 30. And by cancelling a factor of 10 from both the numerator and denominator, this becomes 60 over three, and 60 divided by three is 20.

If one thirtieth of 600 is 20, then multiplying by seven will give seven thirtieths. And as two multiplied by seven is 14, this means that 20 multiplied by seven is 140. So we got the same answer but in a different way.

Next, we need to find the number of passengers who have brown eyes, so we need to calculate 60 percent of 600. There are again lots of different ways that we could do this. For example, we could remember that 60 percent literally means 60 out of 100. So we could write this as the fraction 60 over 100, which cancels to six over 10, which is equal to the decimal 0.6. We could then multiply 0.6 by 600 to give our answer.

To do this, we need to remember that 600 is equal to 100 multiplied by six. It doesn’t matter which order we multiply numbers together in. So first, we could multiply 0.6 by 100, giving 60, and then multiply this by six, which would give 360. This is because six multiplied by six is 36, so six multiplied by 60 is 360.

Perhaps a more straightforward way of finding 60 percent of 600 would be to first find 10 percent by dividing 600 by 10. This would give 60. To find 60 percent of 600, we’d then need to multiply our value for 10 percent by six, giving 360 as before.

To work out the total number of passengers who have either blue or brown eyes, we’d need to add 140 to 360. We could do this mentally or using a column addition method, and it gives 500. As the rest of the passengers have green eyes, we’d then need to subtract this number from the total, which was 600. 600 minus 500 is 100, so there are 100 passengers on the plane who have green eyes.

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