Intermath | Workshop Support

Write-up


Title
Gretelís Goldfish

Problem Statement
Hansel has goldfish that quadruple, or become four times as many, every month. Gretel has goldfish that increase by 20 every month. Right now, Hansel has 4 goldfish and Gretel has 128 goldfish. In how many months will they have the same number of goldfish? Show how you arrived at your answer.


Problem setup

How long will it take Hanselís four goldfish, which quadruple each month, to equal the number of Gretelís goldfish that increase by 20 each month.

 

Plans to Solve/Investigate the Problem

I set up a spreadsheet with a formula for Hanselís goldfish to quadruple each month and Gretelís goldfish to add 20 each month.

 

Investigation/Exploration of the Problem

 

Hansel

Gretel

0

4

128

1

16

148

2

64

168

3

256

188

4

1024

208

5

4096

228

6

16384

248

7

65536

268

The numbers donít easily match up to be the ďsame.Ē  If these goldfish had gestational periods, then it could take a full month for them to magically reproduce.  So, I tried to figure out if maybe they were the same at a certain week.

Weeks

Hansel

Gretel

0

4

128

1

 

133

2

 

138

3

 

143

4

16

148

5

 

153

6

 

158

7

 

163

8

64

168

9

112

173

10

160

178

11

208

183

12

256

188

But the answer is ďno.Ē  But, if it was by weeks, then the number would be closest to each other between weeks number 10 and 11.  Of course, we still donít know if these are live goldfish or cracker goldfish.  I mean, we are talking about Hansel and Gretel, here.  I imagine if we had to, we could break this down into days and hours, but the variables are unclear about the definite direction.

 

Extensions of the Problem

This same concept can be used to re-iterate saving money and the impact of interest rates.

Author & Contact
Lorri Worman
lworman@rockdale.k12.ga.us

Link(s) to resources, references, lesson plans, and/or other materials
A Penny A Day
Rule of 72