PLEASE DO NOT USE ALGEBRA

Question

Container A contains 3 times as much water as Container B. Ron pours

1.25 quarts of water from Container A into Container B. Container A now

contains twice as much water as Container B.

a) How many quarts of water are there in all?

 

 

 

b) Ron mixes the water with 1.5 quarts of lemon juice to make lemonade.

He pours the lemonade into containers of 1/2 quart each. How many

containers does Ron need?

 

Answer 1

We will need to represent 0.25 quarts somehow.  How about cups (c)??

 

And, let's work Part-a backward.

 

After pouring, Container A contains twice as much water as Container B.

In groups, this looks like this:

  Container A:     cc        cc       cc   . . .    cc

  Container B:     c          c         c   . . .     c

 

But before pouring, Container A contained 3 times as much water as Container B.

That looked like this:

  Container A:     ccc      ccc      . . .  ccc

  Container B:      c         c        . . .   c

 

The total amount of water did not change.  The number of groups increased by 5 because Ron poured 1.25 quarts (that is, 5 cups) from Container A into Container B. 

  There are 3 c's in new groups and 4 c's in old groups.

     3*(new number of groups) = 4*(old number of groups)

     3*(old number of groups + 5) = 4*(old number of groups)

     3*(old number of groups) + 15 = 4*(old number of groups)

     15 = (old number of groups)

               [Well, this is Algebra without "x"'s.]

 

The number of cups is 15*4=60 cups.  This is 15 quarts.

 

Check:

   Before:

       Container A contains 45 cups           (3*15)

        Container B contains 15 cups          (1*15)

     This is 3 times as much.

   After:

       Container A contains 40 cups          (2*20)

       Container B contains 20 cups          (1*20)
    This is twice as much.

 

 

b) Ron mixes the water with 1.5 quarts of lemon juice to make lemonade.
He pours the lemonade into containers of 1/2 quart each. How many
containers does Ron need?

 

    15 quarts + 1.5 quarts = 16.5 quarts

      16.5 / (1/2) = 33 containers