Saturday, 25 February 2017

Quibans 56: All you can eat

Thanks to Jamie for pointing me to this article, from the Daily Mail online:

How to BEAT the all-you-can-eat buffet: The expensive foods you should fill up on (and the cheap ones to avoid to get your money’s worth) 
The hacks were revealed on Channel 4's new documentary The 2,000,000 Calorie Buffet.The show, which airs on Monday, reveals that Brits spend around £4,000 on dining out a year.One of the most popular options for eating out is the all-you-can-eat buffet as you pay one low price - usually between £12 and £15 - and can eat as much as you like.But there's money to be made in this business - on a typical night, one of these restaurants can make £12,000. The show looks at the best ways to beat the buffet, as well as the tactics the restaurants employ to earn as much profit as they can.

Questions:
1) Is it reasonable that “Brits spend around £4,000 on dining out a year”?
2) How much do we spend on food in a year?
3) Where does “2,000,000 Calories” come from?

Answers:
1) This seems massively high.  It is about £10 per day (exactly £10 per day would be £3650 per year, which could sensibly have been rounded.  Taking the £12 cost of a buffet meal, that makes £4380, which also rounds to £4000, so you could have a buffet meal every day of the year.  Alternatively it is about £80 per week, which seems like an expensive meal to me. 

2) This is a nice opportunity to think about supermarket shopping (take the family bill for the week, subtract non-food items and then divide by the number of members of the family, add on other purchases (coffee, soft drinks, snacks, etc).

3) If a restaurant makes £12,000 per night and it costs about £12 then that requires 1000 customers.  If the average calorie intake per day is 2000 then multiplying the two gives 2 million calories.  (I have no idea whether that is where this comes from, but it seems plausible!)



Monday, 6 February 2017

Quibans 55: Super Bowl in Space

From the BBC website:

Super Bowl: Astronaut throws football '564,644 yards'
Nasa has released a video of the International Space Station crew preparing to watch the Super Bowl from 250 miles above Earth.


Show the first 3 seconds (and then stop it!) of the video.  The BBC article is here:
The video is also available on YouTube:

So: how fast is the International Space Station moving?
Given that the circumference of the earth is about 25,000 miles, how long does it take the space station to orbit the earth?

Answers:
It travels 564,644 yards in about 64 seconds.  (Use the fact that the ball is released about 5 seconds into the video and the video says it lasts 1 minute 9 seconds.
Divide the number of yards by 64 to get 8822.563 yards per sec
There are 1760 yards in a mile.  So this is 5.01282 miles per sec
Multiply by 3600 to get 18046.15 mph
Given the estimates involved, round this off to 18,000mph.

The circumference of the earth is 25,000 miles, which gives a radius of 25,000 / (2*pi) = 3979
Add 250 (height of orbit of ISS) and then multiply by 2*pi() to get the circumference of the orbit = 26600.  Divide this by the speed to get 1.5 hours for one orbit.

(According to Wikipedia, one orbit lasts 92 minutes.)

Monday, 30 January 2017

Quibans 54: Terrorism vs gun violence

While this is a news story from a few months ago, it seems rather relevant right now.  From CNN:
American deaths in terrorism vs. gun violence in one graph
October 3, 2016

Using numbers from the Centers for Disease Control and Prevention, we found that from 2001 to 2014, 440,095 people died by firearms on US soil. (2014 is the most recent year for which the CDC has data for deaths by firearms.) This data covered all manners of death, including homicide, accident and suicide.
According to the US State Department, the number of US citizens killed overseas as a result of incidents of terrorism from 2001 to 2014 was 369.
In addition, we compiled all terrorism incidents inside the United States and found that between 2001 and 2014, there were 3,043 people killed in domestic acts of terrorism. This brings the total to 3,412.



Possible questions:
1) How many years have been included?
2) Why is this starting point relevant?
3) What percentage of the deaths by terrorism took place in 2001?
4) What percentage of the deaths by firearms occurred in 2014?
5a) Of all of the deaths in 2014, what percentage of them involved terrorism?
5b) Rewrite part (a) in the form “1 in ###”
6) What percentage of the terrorism incidents took place on US soil?
7) What other questions can you ask/answer?

Answers:
1) How many years have been included?  14 years (not 2014 – 2001 = 13).
2) Why is this starting point relevant?  The September 11th attacks took place in 2001.
3) What percentage of the deaths by terrorism took place in 2001?  87.6%
4) What percentage of the deaths by firearms occurred in 2014?  7.6%
5a) Of all of the deaths in 2014, what percentage of them involved terrorism?  0.095%
5b) 1 in 1050
6) What percentage of the terrorism incidents took place on US soil?  89%




Thursday, 26 January 2017

Quibans 53: Trump's Wall

From the Guardian:




Mission: fill in the gaps.

We discussed the equivocating language that has been used here ('likely', 'assuming', 'could cost', etc).  We also talked about other Walls (in the West Bank, Cyprus, Korean peninsula, Berlin).

Are the figures in the image reasonable ones?  Will it really be that high?  Can a wall that high really be only a foot thick?

Our calculations gave us about 8.9 cubic metres of concrete and a total estimated cost of $38 billion.  Reasonably, my class wanted to round this off to $40 billion.  The original Guardian article is linked below.  Here is the image:



Source: https://www.theguardian.com/world/2017/jan/25/mexico-enrique-pena-nieto-trump-border-wall 

Saturday, 7 January 2017

Quibans 52: Big Mexican Food

Two articles, the first taken from the Daily Telegraph, the second from the international news organisation Reuters:

Families line up for slice of 4,724-metre long cake to celebrate Three Kings Feast

Several thousand people gathered in Mexico City's huge Zocalo plaza on Thursday evening to partake in a gigantic Three Kings Day cake known as a "rosca."
The monumental rosca weighed in at 9,371 kilos (20,660 lbs) and measured 4,724 metres long (15,500 ft) before it was cut up into giant pieces and given to anyone wanting a piece.

Mexico makes mammoth 'torta sandwich'

An army of chefs in Mexico City on Wednesday (July 27) crafted a 66-metre (###-foot) monster "torta" sandwich - making it the biggest sandwich of its kind ever made in Latin America.
Local authorities and dozens of local business rolled up their sleeves to prepare the mega sandwich in less than 4 minutes - known as "torta" in Mexico.
Despite its super size, the sandwich didn't quite make it into the big league.
According to the Guinness Book of World Records, the largest sandwich ever made was in 2005 in the United States and weighed ### kg (11,993 lb), while the honor of the longest sandwich goes to Lebanon with a sandwich over 7.5 meters (2,411 feet) long in 2011.


What questions can be asked/answered?
Here are a few ideas:
1) What is the conversion between kg and lbs in the first article?
2) What is the conversion between metres and feet in the first article?
3) What is the weight of cake per metre?
4) How many pieces of cake might there be?
5) In the second article, how long (in feet) was the torta?
6) What was the weight in kg of the biggest sandwich ever made?
7) What is the error in the final sentence?
8) How did the longest sandwich compare with the cake?
9) If you could keep it fresh, for how long would the cake/sandwich feed one person?

Answers:
1) 1kg = 2.205 lb
2) 1m = 3.28 ft
3) 1.98kg per metre
4) The cake can’t be more than about ½ metre wide (otherwise it wouldn’t fit in an oven), so we might assume an area of 4724 x ½ = 2362 square metres.  If each piece has an area of 10cm by 10cm then there will be 100 pieces in a square metre.  This would give 236200 pieces; about a quarter of a million!
5) Using the conversion from the first article we get 216.55m.  The second article gives 216-foot.
6) Using the conversion from the first article we get 5440kg, which is what the second article gives.
7) In the final sentence the unusual spellings (‘honor’ and ‘meter’) are because this is using American English.  The error is the conversion: 7.5 meters (2,411 feet).   2411 feet is actually 735 metres.
8) Using the measurements given in feet, the longest sandwich is 15.6% of the length of the cake.
9) In Subway they sell ‘foot-long’ sandwiches.  One of those per day would mean the sandwich would last 2411 days, which is 6 years and 31 weeks.
The cake would last for 80 years if you had 8 pieces per day.




Saturday, 24 December 2016

Quibans 51: Monster Carrots

From the Cambridge News:
Frenzied Friday: Supermarkets to see surge in last minute food shoppers before Christmas
Supermarkets across the country are bracing themselves for rush of last minute Christmas food shoppers today (December 23).
Already dubbed 'Frenzied Friday', many stores are expected to have their busiest day of the year as millions of customers stock up for some Christmas feasting.
Tesco's has predicted that over 10 million customers will be visiting its stores throughout the day, around 15,000 per minute.
Tesco expects to selling 40 million Brussels sprouts across today and yesterday as well as 3.5 million carrots - enough to stretch around the world 11 times.

The big thing here is having an idea about the size of numbers. An initial question (before showing the other questions):

Question zero) Do the numbers in the question seem reasonable ones?


Questions:


Q1) “10 million customers […], around 15,000 per minute”. What does this tell us?

Q2) The distance from the north pole to the equator is 10,000 km. How big would a carrot need to be if the news story is accurate?


Answers:

Q0) The number of customers seems reasonable, but the number of carrots seems to be much too small to stretch around the world 11 times.

Q1) 10 million divided by 15,000 equals just over 11 hours. So either Tesco stores are open for 11 hours a day, or they have sensibly decided that more people shop during the day rather than in the middle of the night.

Q2) The circumference of the earth is 40 million metres. 11 times round the world would be 440 million metres. Dividing that by 3.5 million carrots gives an average carrot-length of 126 metres. Monster carrots! 12.6cm seems more reasonable for the length of a carrot so dividing by 1000 would be useful.

There are three easy ways to do this: make an error and assume the circumference of the world is actually 40,000 metres (rather than km); sell 3.5 billion carrots, or say that the carrots will go 0.011 times round the world!

If you decide that the Brussels sprouts should be included (the sentence is potentially ambiguous, even if you ignore the grammatical typo) then that doesn’t help (unless you have Monster Sprouts…).

Source: http://www.cambridge-news.co.uk/news/cambridge-news/frenzied-friday-supermarkets-see-surge-12364134


Friday, 16 December 2016

Quibans 50: A million cyclists

From the Cambridge News:
One million cyclists in Cambridge have passed Parker's Piece bike counter this year
14 Dec 2016
One million cyclists have ridden past the cycle counter in Parker's Piece since January, breaking the all-time record.
 
Roxanne de-Beaux, of the Cambridge Cycling Campaign, said last year the total had fallen frustratingly short, coming in 50,000 under the million mark.
Cllr Noel Kavanagh, cycling champion at Cambridgeshire County Council, said the number was brilliant news, but not a total surprise.
"I am not surprised," he said. "I cycle through it several times and have noticed the total going up. Most days, it is two or three thousand. I think this is really good.”
The counter was put in place in 2014, in part to commemorate the historic start of the 2014 Tour de France in the city.

Here are some of the comments under the article:

Commenter 1:
Interesting to note that a person who uses their car exclusively probably pays less per mile in VED, than a car owning cyclist... in other words, a car owning cyclist pays more "road tax" per mile than average Joe Car.
Commenter 2:
"a car owning cyclist pays more" - interesting, I never thought of it like that.
Commenter 1:
I have a car and a bicycle. I do ~2000 miles in my car (I cycle most places within 5 miles) and pay ~£220 VED, thus pay ~##p per mile.
The average car does around 8000 per year, with an average VED of £166, so ~##p per mile. (source for averages... Google).
So, thus as mainly a cyclist in town, I pay a lot more road tax per mile than most car drivers. Given, there are a lot of caveats to this.


The comments under a Cambridge News article that involve bikes often turn into a cyclist vs driver argument. This little exchange between two commenters involves some nice Core Maths skills!

Possible questions:


1) What does the headline mean?

2) How many bikes pass this point per day? What are the difficulties with carrying out this sort of calculation?

3) What will the counter read at the end of the year?

4) What is the percentage increase from last year?

5) Is the councillor correct with his statements?

6) VED is “vehicle excise duty” – commonly referred to as “car tax” or “road tax”. The symbol ~ means “approximately”. What are the numbers I have blanked out in the comments?



Answers:


1) It doesn’t mean that there were a million cyclists. Just that a bike has been read by the sensor a million times. One person cycling past it twice each day would contribute 365 x 2 of these, for example.

2) There are 31-13 = 18 days to go until the end of the year. This was a leap year, so there have been 366-18 = 348 days. 1 million divided by 348 = 2874 per day.

I have no idea whether more people cycle during the week (getting to work), or at the weekend (because they have time to do so). Maybe best to say it is between 2500 and 3000 per day?

We also don’t know when the figure of a million was reached (we only have the date of the article to go on.)

3) What will the counter read at the end of the year? Again, we don’t know whether more people cycle close to Christmas (for leisure reasons, coming back from Christmas parties, etc), or fewer (they drive because they won’t fit the presents they buy in their basket, they are away visiting relatives, etc. If we go for 2500 per day between now and the end of the year then that would be an additional 45000.

4) What is the percentage increase from last year? 1,045,000 this year compared to 950,000 last year. Dividing these gives 1.1, which means a 10% increase.

5) Is the councillor correct with his statements? “have noticed the total going up” – yes- that is correct (!). “Two or three thousand” is right too.

6) ~11p compared to ~2p.



Source: http://www.cambridge-news.co.uk/news/cambridge-news/record-breaking-one-million-cyclists-12321840