Video: AQA GCSE Mathematics Higher Tier Pack 5 • Paper 1 • Question 7

The following is a recipe for 20 crepes: 3 eggs, 250 g of flour, 500 ml of milk. Rob has 12 eggs, 1 kg of flour, and 1.5 l of milk. What is the maximum number of crepes he can make?

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Video Transcript

The following is a recipe for 20 crepes: three eggs, 250 grams of flour, 500 millilitres of milk. Rob has 12 eggs, one kilogram of flour, and 1.5 litres of milk. What is the maximum number of crepes he can make?

To answer this question, we’ll need to work out how many batches of the recipe, that’s how many batches of 20 crepes that Rob can make with each individual ingredient. Let’s begin with the eggs. Rob has 12 eggs and the recipe call for three eggs. We can, therefore, work out the number of batches that Rob can make with these eggs by dividing 12 by three. That’s four. So he can make four batches of 20 with his eggs.

Let’s repeat this with the flour. He has one kilogram of flour and each recipe calls for 250 grams. We can only repeat that process from before if the units are the same. So we remind ourselves that each one kilogram of flour is the same as 1000 grams. And we divide 1000 by 250 since that’s the amount of flour required for a batch of pancakes. 1000 divided by 250 is four. So he can make four batches of pancakes with his flour.

Now this might have been a sum you could do in your head. However, if not, remember that we can write division as a fraction. 1000 divided by 250 can be written as 1000 over 250. We then simplify as far as possible. First, we can divide both the numerator and the denominator by 10. And 1000 over 250 is the same as 100 over 25. At this point, you might be able to do that in your head. If not, we can divide both 25 and 100 by five. That gives us 20 over five or 20 divided by five, which we of course know is four. So that’s another way of working out 1000 divided by 250.

Finally, let’s work out how many batches Rob can make with his milk. One litre is equivalent to 1000 millilitres. We can work out how many millilitres there are in 1.5 litres then by multiplying by 1000. When we multiply by 1000, we move the digits to the left three places. So 1.5 multiplied by 1000 is 1500 millilitres. Each batch requires 500 millilitres of milk. So we’re going to divide 1500 by 500.

We could again use the fraction method. But we recall that 15 divided by five is three. So that means that 15 hundred or 1500 divided by 500 is three. So he can make three batches of pancakes with his milk. This means the most pancakes he can make is three batches. He has enough flour and eggs for more. But he doesn’t have enough milk.

Each batch makes 20 pancakes. So he can make three times this amount. Three multiplied by 20 is 60. So he can make 60 pancakes or 60 crepes with his ingredients.

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