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### Cost of a Ruler

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Date: 08/01/97 at 23:56:44
From: Anonymous
Subject: Cost of a Ruler

Dr. Math,

I'm an elementary educator, and one of my parents (who happens to be
this problem?

Alice and Betty want to buy the same kind of ruler but Alice is 22
cents short and Betty is 3 cents short.  When they combine their
money, they still do not have enough money.  What is the most the
ruler could cost?

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Date: 08/07/97 at 16:32:28
From: Doctor Rob
Subject: Re: Cost of a Ruler

Nice problem!

Let A be the amount of money Alice has, and B the amount Betty has.
Then the cost of the ruler is C = A + 22 = B + 3.

This tells you that B = A + 19.  When Alice and Betty put their money
together, they have A + B = 2*A + 19 < C = A + 22, so
A < 3 and B < 22.

The cost of the ruler will be largest when A or B is largest. The
largest amount of money Alice could have is 2 cents, and the largest
Betty could have is 21 cents.  The maximum cost of the ruler is then
2 + 24 = 21 + 3 = 24 cents.

-Doctor Rob,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
Middle School Algebra
Middle School Word Problems

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