Chapter 9A – Problem Solving Worked Solutions

Ex. 9A Q.3

My friend and I are trying to work out whether it is better to take a million dollars now or to collect the money after 21 days by doing the following. Put in a dollar on the first day, double that dollar the next day, then double the previous day's dollars and continue this for 21 days. What would you advise? (Use mathematics to explain your answer.)

Step One: Write down all the information that you have.

Day # Amount of Money1 12 23 44 85 166 327 64

Step Two: Try to identify a pattern that will lead to a formula. You didn’t need to go any further with the above pattern, as this should be enough for you to find the formula from.

Day # Amount of Money Pattern1 1 20 = 12 2 21 = 23 4 22 = 44 8 23 = 85 16 24 = 166 32 25 = 327 64 26 = 64

Step Three: Discovering the pattern and applying a rule/formula: You might be asking how I got the indices? iI looked at the numbers. In this case, I just knew. However, if you notice that you can multiply the previous number by the same number (in this case 2), you know it is going to be indices.

There is a pattern. The exponents are 1 less than the number day it is. Therefore we can form a formula.

Chapter 9A – Problem Solving Worked Solutions

Step Four: Test the formula.

an−1=Amounti .e . a is 2, n is the day number .so for 21 days, we substitute into the formula .a21−1=a20

As a = 2, the sum is 220

You type this into the calculator to get your answer .Ans=$1048576

Step Five: Justification of answer

Now you explain your answer to answer the question fully.

You now need to write down what you have found in sentences.i .e . You will earn/save more money over 21 days by doubling the amount every day, then you will by keepingthe million dollars at the start .

Chapter 9A – Problem Solving Worked Solutions

9A – Question 4n c i1 5 -22 10 -43 15 -64 20 -85 25 -106 30 -127 35 -148 40 -169 45 -1810 50 -2011 55 -2212 60 -2413 -2614 -2815 -3016 -3217Number of i + number of c = 20

Step 1: Write down all the information.Step 2: Write down the problem: i.e. number of I + number of c = 20Step 3: Trial and error to find the answer.Step 4: Check to make sure there is not a better solution.

Chapter 9A – Problem Solving Worked Solutions