Title
Gretel’s 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 Hansel’s four goldfish, which quadruple each month, to
equal the number of Gretel’s goldfish that
increase by 20 each month.
Plans to
Solve/Investigate the Problem
I set up a spreadsheet with a
formula for Hansel’s goldfish to quadruple each
month and Gretel’s 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 don’t
easily match up to be the “same.” 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 “no.”
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 don’t 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 reiterate 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
