Cost of a Ruler

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 
an accountant) is trying to stump me.  Can you please help me with 
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?

Thank you for your help.

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/