Money Problem

1
Money Problem Solving
2
Put Your Thinking Cap On!
On my 12th birthday my grandmother gave me a
choice. She handed me one silver dollar and one
dime. Then, she told me that if I picked the
silver dollar she would send me one more silver
dollar than the year before. So for my 13th
birthday I would get 2 silver dollars. Next, she
said that if I chose the dime she would send me
twice as much money as the year before. So for
my 13th birthday I would get twenty cents. Which
choice would have earned me the most money on my
17th birthday?
3
Which problem solving strategy would work best
for me for this problem?
Make a Table
4
The silver dollar earned more so far...
13 14 15 16 17
Silver Dollar 2.00 3.00 4.00 5.00 6.00
Dime 0.20 0.40 0.80 1.60 3.20
5
Which choice would have been better on my 22nd
birthday?
6
At 22 the dime is a better choice!
18 19 20 21 22
Silver Dollar
Dime
11.00
8.00
9.00
10.00
7.00
6.40
12.80
51.20
25.60
102.40
7
How do we know the dime was a better choice?
8
Try to solve this next challenging problem
with your team!
9

You're sitting in math class, minding your own
business, when in walks a success story from your
school. He's made it big, and now he has a job
offer for you.

• You'll have your choice of two payment options
• One cent on the first day, two cents on the
  second day, and double your salary every day
  thereafter for the thirty days or
• Exactly 1,000,000. (That's one million dollars!)
  

10
HINT
30 days is a long time and would make a VERY
large table. Break the table into 1st week, 2nd
week, 3rd week, 4th week, and the 29th and 30th
day on the last table to find the pennies. That
means you will have 5 tables altogether.
11
At the end of the first week


.01
.01
.02
.03


.04
.07


.08
.15
.16
.31
.32
.63
.64
1.27
12
Option 2
250,000.00
13
At the end of the second week
2.55
1.28
2.56
5.11
10.23
5.12
10.24
20.47
20.48
40.95
40.96
81.91
81.92
163.83
14
Option 2
500,000.00
15
At the end of the third week


163.84
163.84
327.68
655.35

1310.71
655.36

2621.43
1310.72
2621.44
5242.87
5242.88
10485.75
10485.76
20971.51
16

We're getting into some serious money here now,
over 20,000, but still nowhere even close to a
million. And there's only 10 days left. So it
looks like the million dollars is the best deal.
Of course, we suspected that all along.  




17
Option 2
750,000.00
18
At the end of the fourth week



20971.51
41943.03
41943.04
83886.07

83886.08
167772.15
167772.16
335544.31

335544.32
671088.63
1342177.27
671088.64
1342177.28
2684354.55
19
Option 2
1,000,000.00
20

Hold it! Look what has happened. What's going on
here? We went from 21 000 to over a million in 6
days. This can't be right. Let me check the
calculations. No, I can't find any mistakes. This
is amazing. Look how fast this pay is growing.
Let's keep going. I can't wait to see what the
total will be.




21
At the end of the 30 days




2684354.56
5368709.11

5368709.12
10737418.23
22
In 30 days, it increases from 1 penny to over 10
million dollars. That is absolutely amazing.