Baseballs, Buckets, and Milk Cartons

Date: 10/09/2001 at 16:53:13
From: Laura
Subject: Algebra; Equations

The question is:

The mass of a baseball is 50g. What is the mass of a bucket when...

   2 buckets = 6 blocks
   1 bucket + 1 block = 2 milk cartons
   2 baseballs = 1 milk carton

I figured out that 1 milk carton = 100g

   2 mc = 200g   1bucket+1ball = 200g  

I can't figure out how to find the answer. Please help!
Laura

Date: 10/10/2001 at 11:30:11
From: Doctor Ian
Subject: Re: Algebra; Equations

Hi Laura,

You're on the right track. If the mass of a baseball is 50 grams, then 
the mass of a milk carton must be twice that, or 100 grams.  

So the mass of a bucket and a block must be twice that again, or 200 
grams.  

Here's where it gets tricky.  Let's look at the two equations

    2 buckets          = 6 blocks

    1 bucket + 1 block = 200 g

The first equation is the same as saying that

    1 bucket            = 3 blocks

which is the same as saying that

    1 bucket - 3 blocks = 0

So now we have these two equations:

    1 bucket - 3 blocks = 0

    1 bucket + 1 block  = 200 g

This tells you that a difference of 4 blocks is the same thing as a 
difference of 200 g.  

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/