Video: AQA GCSE Mathematics Foundation Tier Pack 2 • Paper 3 • Question 9

A travel agent offers gold, silver, and bronze packages for holidays to Florida. 210 customers purchased a holiday package to Florida; 3/5 of the customers purchased the bronze package, and 1/6 of the customers purchased the gold package. Work out the number of customers who purchased the silver package.

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Video Transcript

A travel agent offers gold, silver, and bronze packages for holidays to Florida. 210 customers purchased a holiday package to Florida. Three-fifths of the customers purchased the bronze package. And one-sixth of the customers purchased the gold package. Work out the number of customers who purchased the silver package.

We were told that there were 210 customers who purchased a holiday package. Of these, three-fifths purchased the bronze package. Therefore, we need to calculate three-fifths of 210. This will tell us the number of customers who purchased the bronze package.

The word “of” in mathematics means multiply or times. This means we need to multiply three-fifths by 210. Typing this into our calculator gives us an answer of 126. Therefore, 126 customers purchased the bronze package.

An alternative method to calculate a fraction of an amount if we didn’t have a calculator is to divide by the denominator and then multiply the answer by the numerator. In this case, to divide 210 by five and multiply our answer by three. This would also give us an answer of 126.

The number of customers who purchased the gold package was one-sixth of the total customers. Therefore, we need to calculate one-sixth of 210. Once again, we can do this by multiplying the fraction by 210. One-sixth multiplied by 210 is equal to 35. Therefore, 35 out of the 210 customers purchased the gold package.

The question asked us to calculate the number of customers who purchased the silver package. As there were 210 customers in total, we need to add the number of customers who purchased the bronze package and those who purchased the gold package and subtract the answer from 210. Adding 126 and 35 gives us 161. Subtracting this from 210 gives us an answer of 49.

We can therefore conclude that 49 customers bought the silver package. We could write this as a fraction, as 49 out of 210 customers bought the silver package. This fraction can be simplified as both the numerator and denominator are divisible by seven. 49 divided by seven is equal to seven. 210 divided by seven is equal to 30, as 21 divided by seven equals three. This means that seven thirtieths of the customers purchased the silver package.

We can use this to check our answer of 49 customers. We do this by calculating seven thirtieths of 210. Seven thirtieths multiplied by 210 is equal to 49. So our answer of 49 customers was correct.

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