In the previous section, we looked at working out the required quantities of the different ingredients required to make a certain number of cakes. In this section, we are going to be looking at questions whereby we are given the quantities of ingredients that an individual has, the recipe for making a certain number of cakes and will be asked to find the greatest number of cakes that our individual can make.

We answer questions like this by working out what multiple of the ingredients we have compared to the recipe. We work this out by dividing the quantities of the ingredients that we have by the quantities of the ingredients that are required in the recipe. We then compare values and the number of times that we can make the recipe will be limited by the ingredient that we have the lowest multiple of. We then work out the maximum number of cakes that we can make by multiplying the lowest multiple of the recipe by the number of cakes that the recipe makes.

This will all make more sense after we have looked at a few examples.

We answer questions like this by working out what multiple of the ingredients we have compared to the recipe. We work this out by dividing the quantities of the ingredients that we have by the quantities of the ingredients that are required in the recipe. We then compare values and the number of times that we can make the recipe will be limited by the ingredient that we have the lowest multiple of. We then work out the maximum number of cakes that we can make by multiplying the lowest multiple of the recipe by the number of cakes that the recipe makes.

This will all make more sense after we have looked at a few examples.

**Example 1**

I have these quantities of the following ingredients:

- 6 eggs
- 500 g of flour
- 300 g sugar

The recipe below makes 10 cakes.

I am going to make as many cakes as possible. What is the greatest number of cakes that I can make? You may use a calculator.

The first step in answering this question is to work out what multiple of the recipe we have for each of the ingredients. We can find this out by dividing the quantity of the ingredients that we have by the quantity of the ingredients required in the recipe. Let’s work the multiple of the recipe that we have for the eggs. We are told in the question that the individual has 6 eggs and the recipe requires 2 eggs. Therefore, we work out the multiple of the recipe that we have by dividing what the individual has (6) by what the recipes requires (2), which gives us 3. This tells us that we have 3 times the quantity of eggs needed for the recipe.

We now do the same for the other ingredients and the working is shown below.

The first step in answering this question is to work out what multiple of the recipe we have for each of the ingredients. We can find this out by dividing the quantity of the ingredients that we have by the quantity of the ingredients required in the recipe. Let’s work the multiple of the recipe that we have for the eggs. We are told in the question that the individual has 6 eggs and the recipe requires 2 eggs. Therefore, we work out the multiple of the recipe that we have by dividing what the individual has (6) by what the recipes requires (2), which gives us 3. This tells us that we have 3 times the quantity of eggs needed for the recipe.

We now do the same for the other ingredients and the working is shown below.

The lowest multiple of the ingredients that we have is 2 (which is from the sugar). This means that we can only make 2 lots of the mixture because we will run out of sugar.

The recipe makes 10 cakes and we have just worked out that we can make 2 lots of the recipe. Therefore, we can work out the maximum number of cakes that we can make by multiplying 2 (the number of times that we can make the recipe) by 10 (the number of cakes a recipe makes).

The recipe makes 10 cakes and we have just worked out that we can make 2 lots of the recipe. Therefore, we can work out the maximum number of cakes that we can make by multiplying 2 (the number of times that we can make the recipe) by 10 (the number of cakes a recipe makes).

The maximum number of cakes that we can make is 20.

**Example 2**

I have these quantities of the following ingredients:

- 225 g breadcrumbs
- 2 kg of beef
- 7 eggs
- 2 bunches of fresh parsley

The recipe below makes 8 meatballs.

I am going to make as many meatballs as possible. What is the greatest number of meatballs that I can make? You may use a calculator.

The first step in answering this question is to work out what multiple of the recipe we have for each of the ingredients. We can find this out by dividing the quantity of the ingredients that we have by the quantity of the ingredients required in the recipe. When we are completing this calculation, we need to make sure that the units are consistent. For example, we are told that we have 225 g of breadcrumbs and the recipe requires 75 g of breadcrumbs. These are both measured in grams (g), which means that we can divide 225 g by 75 g, which tells us that we have 3 times the quantity of breadcrumbs required.

The quantities for the eggs and fresh parsley are consistent, which means that we do not need to change any of the units.

However, we are given the quantity of beef in kilograms (kg) and the amount required in the recipe is in grams (g). In order to work out the number of times that we have the recipe in beef, we need to have consistent units. I am going to have both of them in grams, which means that I need to convert the 2 kilograms of beef into grams. There are 1,000 grams in a kilogram, which means that we convert 2 kg into grams by multiply 2 by 1,000 to give us 2,000 g. Therefore, we have 2,000 g of beef. We now have all of the quantities in consistent units, thus meaning that we can work out the multiplies of the recipe that we have for the different ingredients. The working is shown in the table below.

The first step in answering this question is to work out what multiple of the recipe we have for each of the ingredients. We can find this out by dividing the quantity of the ingredients that we have by the quantity of the ingredients required in the recipe. When we are completing this calculation, we need to make sure that the units are consistent. For example, we are told that we have 225 g of breadcrumbs and the recipe requires 75 g of breadcrumbs. These are both measured in grams (g), which means that we can divide 225 g by 75 g, which tells us that we have 3 times the quantity of breadcrumbs required.

The quantities for the eggs and fresh parsley are consistent, which means that we do not need to change any of the units.

However, we are given the quantity of beef in kilograms (kg) and the amount required in the recipe is in grams (g). In order to work out the number of times that we have the recipe in beef, we need to have consistent units. I am going to have both of them in grams, which means that I need to convert the 2 kilograms of beef into grams. There are 1,000 grams in a kilogram, which means that we convert 2 kg into grams by multiply 2 by 1,000 to give us 2,000 g. Therefore, we have 2,000 g of beef. We now have all of the quantities in consistent units, thus meaning that we can work out the multiplies of the recipe that we have for the different ingredients. The working is shown in the table below.

The lowest multiple of the ingredients that we have is 3 (which is from the breadcrumbs). This means that we can only make 3 times the mixture because we will run out of breadcrumbs.

The recipe makes 8 meatballs and we have just worked out that we can make 3 lots of the recipe. Therefore, we can work out the maximum number of meatballs that we can make by multiplying 3 (the number of times that we can make the recipe) by 8 (the number of meatballs the recipe makes).

The recipe makes 8 meatballs and we have just worked out that we can make 3 lots of the recipe. Therefore, we can work out the maximum number of meatballs that we can make by multiplying 3 (the number of times that we can make the recipe) by 8 (the number of meatballs the recipe makes).

Therefore, the maximum number of meatballs that we can make is 24.