Potato Cake Proportions: Calculating Cheese Costs

Let’s tackle a real-world math problem involving proportions and costs! Natalie, a restaurant chef, is making potato cakes with a specific recipe.

The Recipe Ratios

Natalie’s potato cake mix follows this ratio:

Potato : Cheese : Onion = 9 : 2 : 1

This means for every 9 parts potato, there are 2 parts cheese and 1 part onion (by weight).

Scaling Up to 6000g

Natalie needs to make 6000g of potato cakes in total. First, we need to figure out how much each “part” of the ratio weighs.

• Total parts in the ratio: 9 + 2 + 1 = 12 parts
• Weight of one part: 6000g / 12 parts = 500g/part

Now we know:

• Potato: 9 parts * 500g/part = 4500g
• Cheese: 2 parts * 500g/part = 1000g
• Onion: 1 part * 500g/part = 500g

So, Natalie needs 1000g of cheese.

Calculating the Cost of Cheese

Cheese costs £2.25 for 175g. We need to find the cost of 1000g of cheese.

• Cost per gram of cheese: £2.25 / 175g = £0.012857 (approximately)
• Cost of 1000g of cheese: 1000g * £0.012857/g = £12.86 (rounded to the nearest penny)

Answer: The cost of the cheese needed to make 6000g of potato cakes is £12.86.

If you’re finding ratio problems like this tricky, a private maths tutor for GCSE can provide bespoke help and guidance!

Key Takeaways

• Ratio problems often involve scaling up or down.
• Pay attention to units (grams, pounds, etc.)
• Break down the problem into smaller, manageable steps.