Video: AQA GCSE Mathematics Foundation Tier Pack 2 • Paper 1 • Question 11

In a tennis club, the ratio of men to women is 1 : 1. The ratio of the men who can serve in excess of 80 mph to those who cannot is 2 : 3. There are 10 men in the club who can serve an excess of 80 mph. How many men and women are in the tennis club in total?

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Video Transcript

In a tennis club, the ratio of men to women is one to one. The ratio of the men who can serve in excess of 80 miles per hour to those who cannot is two to three. There are 10 men in the club who can serve an excess of 80 miles per hour. How many men and women are in the tennis club in total?

So the first thing we’re gonna do to help us solve this problem is take a look at the ratio that we’ve got here. That is, two to three. And this ratio is the ratio of men who can serve in excess of 80 miles per hour to those who cannot. So as we’re dealing with a ratio, we deal with it in the order that is written. So therefore, we can say that the two parts refers to 80 plus, so in excess of 80 miles per hour. And the three parts refers to those not 80 plus miles per hour.

Then, next, what we’re told is that there’re 10 men in the club who can serve in excess of 80 miles per hour. So therefore, this piece of information relates to the two parts because it’s talking about men who can serve in excess of 80 miles per hour. So therefore, we can say that two parts is equal to 10 men. So therefore, if we want to find out what one part is worth, we’re gonna divide both sides by two. And that’s cause if we divide two parts by two, we get one part. So therefore, what we do to one side, we have to do to the other. So therefore, we know that one part is equal to five men.

Okay, great, so how can we work out what the total number of men is? Well, to work this out, we’re gonna have to work out the total number of parts in the ratio. Well, the total number of parts is equal to two plus three because we’ve got two parts and three parts which is equal to five. So therefore, we have five parts in total. So therefore, if we want to work out the total number of men, it’s gonna be equal to five multiplied by five. And that’s because we know that one part is equal to five men. And we know that there are five parts in total. So therefore, if we multiply these two together, we have a total number of men of 25.

So great, have we finished the question? Well, no because we’re told to work out how many men and women are in the tennis club in total. Well, we know how many men there are. But how can we work out how many women there are? Well, we can do this using another ratio we’ve been given. And this ratio is that the ratio of men to women is one to one. So therefore, what this means in real terms is that there’s exactly the same number of men as women in the tennis club. So therefore, the number of women in the tennis club is also going to be 25 because as we said the ratio is one to one.

So therefore, the total number of men and women in the club is equal to 25 add 25, which gives a total number of 50.

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