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 Write-up

Title
Kate's \$

Problem Statement
Kate has x quarters and y dimes, a total of 16 coins. She exchanges the x quarters for the number of dimes equal in value to x quarters. She also exchanges the y dimes for the number of quarters equal in value to y dimes. After these exchanges, how many coins does she have?

GPS Alignment

M6P2. Students will investigate, develop, and evaluate mathematical arguments.

M6P3. Students will use the language of mathematics to express ideas precisely.

M7P2. Students will investigate, develop, and evaluate mathematical arguments.

M7P3. Students will use the language of mathematics to express ideas precisely.

M8P2. Students will investigate, develop, and evaluate mathematical arguments.

M8P3. Students will use the language of mathematics to express ideas precisely.

Problem setup

Kate has quarters in one hand and dimes in the other. The total number of coins she has equals 16. She trades in the exact value of her quarters for dimes. She then trades in the exact value of her dimes for quarters. After both of these trades, how many coins does she have?

Plans to Solve/Investigate the Problem

Our initial plan was to write x + y = 16 where x= the no. of quarters and y= the no. of dimes. The number 16 is the total number of coins she started with. We then decided to make an x and y chart putting in the correct values for x quarters and y dimes.

Investigation/Exploration of the Problem

The following is the chart:

Quarters (x)                        Dimes (y)

0                                        16

2                                        14

4                                        12

6                                        10

8                                         8

10                                        6

12                                        4

14                                        2

16                                        0

The only possible correct answer is that Kate started with 6 quarters and 10 dimes. All other combinations will not work because the quarters must equal an amount that ends in 0 and the dimes must equal an amount that is evenly divisible by 25.

So we have 6 quarters =\$1.50 which equals 15 dimes. We have 10 dimes = \$1.00 which equals 4 quarters.  Since she trades her 6 quarters for 15 dimes and her 10 dimes for 4 quarters, her total number of coins is now 19 and this is the final answer.

Extensions of the Problem

We did no extensions with this problem.

Author & Contact
Pam Joseph.
mailto:prj1@aol.com

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