Word problem that looks so simple!

jesuslover · #1 $Old$ 05-21-2008, 03:23 PM

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.

janvdl · #2 $Old$ 05-21-2008, 03:31 PM

Quote:

Originally Posted by jesuslover $View Post$

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 $x$ eggs.
6 baskets contain $6x$ eggs.

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

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

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

$8x = 576$
$x = 72$

Therefore each basket contains 72 eggs and each pail contains 48 eggs.

jesuslover · #3 $Old$ 05-21-2008, 04:39 PM

So...(1/3)(6x) + 6x=576
2x + 6x=576
8x=576
x=72
72 eggs per basket
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!

janvdl · #4 $Old$ 05-22-2008, 12:36 AM

Quote:

Originally Posted by jesuslover $View Post$

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.

Soroban · #5 $Old$ 05-22-2008, 03:57 AM

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?

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

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

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

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

Solve the system of equations.