# Word problem that looks so simple!

• May 21st 2008, 01:23 PM
jesuslover
Word problem that looks so simple!
Hello!
Here is the word problem:
Three pails and 6 baskets contain 576 eggs. All the pails contain 1/3 as many eggs as all the baskets. How many eggs are there in each pail? In each basket?

I tried to figure this one out, but the answers don't fit. I am so horrible at word problems! Could someone explain how to solve this type of problem? I would be most appreciative.
• May 21st 2008, 01:31 PM
janvdl
Quote:

Originally Posted by jesuslover
Hello!
Here is the word problem:
Three pails and 6 baskets contain 576 eggs. All the pails contain 1/3 as many eggs as all the baskets. How many eggs are there in each pail? In each basket?

I tried to figure this one out, but the answers don't fit. I am so horrible at word problems! Could someone explain how to solve this type of problem? I would be most appreciative.

A single basket contains $\displaystyle x$ eggs.
6 baskets contain $\displaystyle 6x$ eggs.

All 3 pails contain a third the number of eggs as all the baskets.
All 3 pails together contain $\displaystyle \left( \frac{1}{3} \times 6x \right) = 2x$ eggs.

So each pail contains $\displaystyle \frac{2}{3}x$ eggs.

Adding it all up we find we have $\displaystyle 8x$ eggs.

$\displaystyle 8x = 576$
$\displaystyle x = 72$

Therefore each basket contains 72 eggs and each pail contains 48 eggs.
• May 21st 2008, 02:39 PM
jesuslover
So...(1/3)(6x) + 6x=576
2x + 6x=576
8x=576
x=72
72(6)=432
432/3=144
144/3=48
48 eggs per pail
I see now! Thank-you! I remember getting 48 before, but, lol, not the 72. That was a big help! Thanks again!
• May 21st 2008, 10:36 PM
janvdl
Quote:

Originally Posted by jesuslover
I see now! Thank-you! I remember getting 48 before, but, lol, not the 72. That was a big help! Thanks again!

You are welcome. :)
• May 22nd 2008, 01:57 AM
Soroban
Hello, Jesuslover!

Another approach . . .

Quote:

Three pails and 6 baskets contain 576 eggs.
All the pails contain 1/3 as many eggs as all the baskets.
How many eggs are there in each pail? In each basket?

$\displaystyle \text{Let: }\;\begin{array}{ccc}P & = & \text{no. eggs in a pail} \\ B &=& \text{no. eggs in a basket} \end{array}$

Then: . $\displaystyle \begin{array}{ccc} 3P &=& \text{total no. of eggs in pails} \\ 6B &=& \text{total no. of eggs in baskets} \end{array}$

We are told that: .$\displaystyle 3P \:=\:\frac{1}{3}(6B)\quad\Rightarrow\quad 3P \:=\:2B$

. . .and that: .$\displaystyle 3P + 6B \:=\:576$

Solve the system of equations.