Pocket Money
Stage: 3 Challenge Level:1
Imagine your family agreed to give you some pocket money every day for a month! You can choose from the following options:
£10 every day
£3 on the first day, £3.50 on the second, £4 on the third, and so on, increasing by 50p per day
1p on the first day, 2p on the second, 4p on the third, and so on, doubling each day.
Without doing any working out, which one would you choose, and why?
In a month with 31 days, how much money would you have by the end of the month, under each system? You may wish to explore using a spreadsheet...
Answers:
The first option would give you 310 pounds. This is because of 31(the number of days) times 10 (the amount you require) is 310 pounds.
The second option gives you 18 pounds in a month with 31 days. One way that I solved this question was make the 50 pence that you get each day and divide it by a pound. This results in. Because 50 pence is half of a pound that would make it 50/100 or to simplify it for problem-solving: ½. but you see that 31 is a prime number which means that it is not divisible by a whole number. We know that 30 divided by 15 is 2 but 30 and 31 only have a one number gap. 31 divided by 2 is 15.5. But as you see we started with 3 then increased by 0.5. So we have to add 3 (which would be 18.5) then subtract 0.5 to get the correct answer which is 18 pounds a month.
The last option gives you 1073741824 pounds a month. You receive this number due to continuous doubling until 31st time.
Here are some questions you might like to consider:
In which months would option 1 be better than option 2?
all months would make option one better than option 2 as you get times 10 any number of days the month has. for example on the shortest month which was December 21st, 2017 you would still 210 pounds that month. but in a 21 day month, you would only receive 13 pounds. This goes for any other month as you only receive 0.5 pounds a day whilst on the other day you receive 10 a day.
If your family stopped your pocket money on day 8, which option would give you the most?
Option 3. That is because you get 128 pounds. option two gives you 6.5 pounds and option 1 gives you 80 pounds.
On which day of the month does option 3 become the most fruitful?
On the tenth day. you receive 512 which is more than option 1 and 2 throughout the entire month.
If you chose option 3, how many days would it be before you became a millionaire?
21 days. On that day you receive 1048576 pounds.