Challenge 7 - Nuts
Challenge 7 is all about problem solving and percentages.
Maths teacher Chris Smith and pupils from Grange Academy are here to help you crack this one.
The Maths Week Scotland Daily Challenges have been set by the Scottish Mathematical Council.
Mr Smith: Today’s problem is all about percentages.
Eilish sells mixed nuts in small bags.
From her wholesaler, she buys walnuts at £8.25 per kg, pecans at £20.85 per kg, Brazil nuts at £16.00 per kg, almonds at £11.80 per kg and hazelnuts at £13.10 per kg.
She mixes them thoroughly and puts the mix into 100g bags, which she sells at her local market.
If she wants to make a 20% profit, what should Eilish charge for a bag of mixed nuts?
And for part two of this puzzle, sometimes, Eilish’s supplier cannot get one of the types of nuts she wants, and so she mixes just the other four types of nut and sells her 100 g bags for £1.62.
Which of the nuts is not available?
Explain your answer.
Pupil One: You'll need to know how many bags Eilish will have in total
Pupil Two: Converting percentages into fractions will help.
Pupil Three: Try and work backwards to find the missing nut.
Pupil Four: Good luck
So here's the challenge:
Part one
Eilish sells mixed nuts in small bags.
From her wholesaler, she buys nuts at the following prices:
- Walnuts at £8.25 per kg
- Pecans at £20.85 per kg
- Brazil nuts at £16.00 per kg
- Almonds at £11.80 per kg
- Hazelnuts at £13.10 per kg
She mixes the nuts and puts them into 100g bags to sell at her local market.
If she wants to make a 20% profit, what should Eilish charge for a 100g bag of mixed nuts?
Part two
Sometimes, Eilish’s supplier cannot get one of the types of nuts she wants, and so she mixes just the other four types of nut and sells her 100g bags for £1.62. She still wants to make 20% profit.
Which of the nuts is not available?
Need a hint?
- You'll need to know how many bags Eilish will have in total.
- Converting percentages into fractions will help.
- Try and work backwards to find the missing nut.
Solution
Worked out the answer? Here's how you can do it.
Mr Smith: Did you work out how much Eilish should charge for a bag of mixed nuts to make 20% profit?
Let’s look at how we got our answers.
There are five types of nuts, so if Eilish mixes a kg of each she will have 5 kg of nuts for which she paid:
£ 8.25 for walnuts + £20.85 for pecans + £16.00 for Brazil nuts + £11.80 for almonds + £13.10 for hazelnuts = a total of £70
A profit of 20% on £70 would be £14.
So Eilish must sell the 5 kg of mixed nuts for £84.
Eilish sells 100g bags. 5 kg is 5000g. And 5000g divided by 100g is 50. Eilish can make up 50 bags.
To make her 20% profit, Eilish needs to sell her 50 bags for £84.
So each bag is priced at £84 divided by 50, which is £1.68
£84 ÷ 50 = £1.68 for a 100g bag.
And did you work out which nut was unavailable if Eilish was selling 100g bags at £1.62?
This time Eilish has 4kg of nuts, which is 4000g.
4000g divided by 100g is 40, so she is selling 40 bags at £1.62 each.
If we work backwards, the sale price of 4 kg of mixed nuts is 40 × £1.62 = £64.80.
£64.80 includes 20% profit, so the price Eilish paid is £64,80 divided by 120 and multiplied by 100. Which equals £54.
The cost of the missing nuts is £70 subtract £54 which equals £16.
So it was the Brazil nuts that weren’t available.
Great job if you cracked this one!
Part 1
Step 1
There are five types of nuts, so if Eilish mixes a kg of each she will have 5 kg of nuts for which she paid:
£ 8.25 for walnuts + £20.85 for pecans + £16.00 for Brazil nuts + £11.80 for almonds + £13.10 for hazelnuts = a total of £70
Step 2
A profit of 20% on £70 would be £14
So Eilish must sell the 5 kg of mixed nuts for £84.
Step 3
Eilish sells 100g bags. Her total amount of nuts is 5 kg which is the same as 5000g.
5000g ÷ 100g = 50.
Eilish can make up 50 bags.
Step 4
So to find the price for each bag, £84 is divided by 50
£84 ÷ 50 = £1.68 per 100g bag
Part 2
Step 5
Did you work out which nut was unavailable if Eilish was selling 100g bags at £1.62?
This time Eilish has 4kg of nuts, which is 4000g.
4000g ÷ 100g = 40
Eilish is selling 40 bags at £1.62 each.
Step 6
If we work backwards, we can find the total sale price of 4kg of mixed nuts:
40 × £1.62 = £64.80
Step 7
£64.80 includes 20% profit. We can now find the price Eilish paid:
£64.80 ÷ 120 x 100 = £54
Step 8
We now know what Eilish paid for four bags of nuts. We can take this away from what she paid for all five bags of nuts, to work out the cost of the missing nuts:
£70 - £54 = £16
£16 is the price of Brazil nuts.
So it was the Brazil nuts that weren’t available.
Maths problem solving. collection
Try out Maths Week Scotland challenges from previous years.
Maths Week Scotland. External Link
Find more maths challenges and activities at the Maths Week Scotland website.
More on Maths Week Scotland 2025
Find out more by working through a topic
- count1 of 8
