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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

I will need to look at the different numbers of fishes for Hansel and for Gretel, for several different months, and compare them until I find what month they will have the same number of fish.

 

Plans to Solve/Investigate the Problem

The first thing I will do is to multiply Hansel’s 4 fish X 4 for 4 months; a nice round number.  Then I will figure out Gretel’s fish for 4 months and compare the two totals. 

 

Investigation/Exploration of the Problem

 

Month

Hansel

Gretel

1

 16

 148

2

 64

 168

3

256

188

4

1024

208

 

I noticed that between month 2 and 3, Hansel’s fish begin to grow much faster than Gretel’s.  I did an Excel spreadsheet, comparing week by week the numbers for Hansel and Gretel’s fish, between Week 8 and Week 12.

 

Week

Hansel

Gretel

1

4

128

2

 

 

3

 

 

4

16

148

5

 

153

6

 

158

7

 

163

8

64

168

9

112

173

10

160

178

11

208

183

12

256

188

 

 

By doing this, I discovered that between week 10 and  week 11, Hansel and Gretel’s fish should be the same number.  Probably about 2 ½ month; so in the 3rd month, they will have the same number of fish.

 

Extensions of the Problem

Now that I’ve learned how to do Excel better, I can use it to help me figure out more hard to solve, brain-boggling problems.

Author & Contact
Meg Ramsey
mramsey@rockdale.k12.ga.us

Link(s) to resources, references, lesson plans, and/or other materials
Link 1
Link 2

 

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