Quibans 79: Nutella Riots

From the BBC:

Nutella 'riots' spread across French supermarkets

A discount on Nutella has led to violent scenes in a chain of French supermarkets, as shoppers jostled to grab a bargain on the sweet spread.

Intermarché supermarkets offered a 70% discount on Nutella, bringing the price down from €### (£3.90) to €1.40.

But police were called when people began fighting and pushing one another.

Some 365 million kilos of Nutella, a hazelnut chocolate spread, is consumed every year in 160 countries around the world.

Here is information about Nutella from the Tesco website:

• Pack size: 750g

Ingredients

Sugar, Palm Oil, Hazelnuts (13%), Fat-Reduced Cocoa (7.4%), Skimmed Milk Powder (6.6%), Whey Powder (Milk), Emulsifier: Lecithin (Soya), Vanillin

50 Portions per jar = 50 x 15g

What can we work out?  Some ideas are below.

.

.

.

.

Q1)  Work out the missing number
Q2)  What is the exchange rate?
Q3)  How many portions are sold each year?

Q4)  How many tonnes of Nutella are sold each year?
Q5)  How many kg of hazelnuts/coca/milk are used each year?

Q6)  Ingredients are listed in order (highest amount to lowest).  What is the smallest percentage of sugar there could be?



Answers

Q1)  Intermarché supermarkets offered a 70% discount on Nutella, bringing the price down from €4.50 (£3.90) to €1.40.
This is interesting because if you do 1.40/0.3 you get 4.67

There has been some rounding going on!  The actual discount is 68.9%

Q2)  £1 = €1.15

Q3)  365 million kg divided by 15g = 24 billion servings.  (That's more than 3 servings per person on the planet)

Q4)  365,000 tonnes  - that's 1000 tonnes per day!

Q5)  Hazelnuts - 47,000 tonnes, Coca - 27,000 tonnes, Milk powder - 24,000 tonnes

Q6)  If the smallest three ingredients are the biggest they can possibly be then they will each be 6.6% and the total of everything other than sugar and palm oil is 46.8%.  The smallest the sugar can be is half of what remains, which is 26.6%.  In reality this is likely to be a big underestimate.

Sources: www.bbc.co.uk/news/world-europe-42826028

https://www.tesco.com/groceries/en-GB/products/250838346

Quibans 78: Expensive wine

In my Spanish class we read a newspaper article about the most expensive wine in the world.  Here is my translation of part of that article:

This is the most expensive wine in the world and it’s made in Spain.
Each bottle of AurumRed ‘gold series’ costs €25,000.  Hilario García produces 300 of these bottles per season, of which he sells 150 immediately and reserves the rest for repeat clients, and there are some of them.
The cellar also produces 6,000 bottles per year of the ‘silver series’, at €2,200 per piece and 3,000 bottles of sauvignon blanc, which is much more accessible at €30.

Questions:

1)      What is the average cost of a bottle of wine from this vineyard?

2)      Comment on the usefulness of this answer

Source: http://www.ideal.es/sociedad/vino-caro-mundo-20171226095403-nt.html

Translation: MD

Original text:

Así es el vino más caro del mundo, que se hace en España

Cada botella de AurumRed serie oro cuesta 25.000 euros.  Hilario García produce al año 300 de estas botellas, de las que comercializa 150 por temporada, y reserva el resto para los clientes que quieren repetir, que los hay.

De la bodega salen también 6.000 botellas al año de la serie plata, a 2.200 euros la pieza, y 3.000 de sauvignon blanc mucho más asequibles, a unos 30 euros.

Quibans 77: Brussels Sprouts at Lidl

On the radio this morning they reported:

Lidl supermarket said it had record UK sales in December, with a rise of 16% on the same period in 2016.
Customers bought about #### tonnes of Brussels sprouts.

I told my class this and said that the first digit of the number of tonnes of sprouts was a 6.  They then worked out a likely number.

What they did is below.

.

.

.

.

.

.

.

.

.

.

.

.

Here is one solution.  Others were shared too.

• Assumption: 1 sprout weighs about 10g.  We know that 1 tonne = 1 million g, so this is 1/100,000 of a tonne.
• Assumption: Each person in the country has 5 sprouts at Christmas.
• Assumption: There are 64 million people in the country.

Multiplying these gives a total sale of 3200 tonnes of sprouts.

Some people buy these from supermarkets (and there are lots of these: Tesco, Sainsburys, Morrisons, Asda, Waitrose, Lidl, Aldi, M&S, Co-Op, Spar), some from local shops and others will grow their own.

Those studying business studies predicted that Lidl might have approx 10% market-share.  

We assumed that this meant they sold 10% of the sprouts too (this is an assumption we need to make.  For example, Iceland (the shop) has more frozen food, so their market share couldn't be used to predict sales for fresh produce).

Lidl would therefore sell 320 tonnes of sprouts.

The next part is the thing I found particularly interesting.  The students pointed out that 320 tonnes was almost exactly midway between 60 tonnes and 600 tonnes.  The halfway point is 330 tonnes.  The students were aware that in an answer as full of estimates as this they couldn't say that their 320 is less than 330 (which is right and sensible), but they were unclear whether they should round up to 600 or round down to 60.

After discussion they were happy with the idea that we usually think in a multiplicative way about our errors in a question like this (so we predicted 5 sprouts per person, but it could have easily been double that).  To get to 600 you multiply by a number less than 2, whereas if you divide by 5 you haven't reached 60.  They decided on 600 tonnes as the answer.

Here is the start of the story (from the BBC News site):

Lidl supermarket said it had record UK sales in December, with a rise of 16% on the same period in 2016.
Customers bought about 600 tonnes of Brussels sprouts

Source: http://www.bbc.co.uk/news/business-42632600