Measuring Four Cups of Flour

Date: 27 Feb 1995 12:14:33 -0500
From: Kay Moore
Subject: We need help!

Dear Dr. Math,
        A third grade class at our school, Ayden Elementary, needs help 
with this problem.
        A cook is making a cake that requires four cups of flour.  She 
only has two measures, which hold 7 cups and 10 cups.  How can she 
use her measures to measure exactly 4 cups?

        We know you will try to help us.
        Thank you,

        Mrs. Moore's Fourth Grade Class

Date: 27 Feb 1995 16:29:13 -0500
From: Dr. Ken
Subject: Re: We need help!

Hello there!

The key to doing this problem is that you have to be kind of tricky, and 
it helps if you've seen this kind of problem before.  Anyway, here's the 
best thing I can think of:  think about what amounts you can get by filling 
one cup up with flour, and then pouring all that will fit from there into the
other cup.  For instance, if you filled up the 10 cup measure with flour, 
and then poured all that will fit into the 7 cup measure, you'd have 3 cups 
left in the bigger measuring cup (because 10 - 7 = 3).  So that's how you 
could get 3 cups.  I'll let you explore this concept some to see how you 
might get 4 cups.  Write back if you still can't figure it out!

Here's another problem for you:  A cook is making a cake, and she needs 
to use 3 cups of milk.  However, she only has one measuring cup (what 
the heck kind of cook only has one measuring cup???  And for that matter, 
what the heck kind of cook only has a 7 cup measure and a 10 cup 
measure???), and that measuring cup is cylindrical and holds 6 cups.  
How can she measure 3 cups of milk using only her 6 cup measure?

-Ken "Dr." Math