Probability

Eanaya

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Aug 22, 2012
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There was a jar of cookies on the table. Amanda ate half the cookies. Then Beth came along and ate a third of what was left in the jar. Christine came by and decided to take a fourth of the remaining cookies. Then Daniel came and took a cookie to munch on. When Eva looked in the jar there were 2 cookies left. How many cookies where there in the jar to begin with?


Not too sure how to solve this fraction problem!!!
 
I tried working in reverse but couldn't figure out how to get rid of the fractions. I let x= # of cookies. I tried your equation but I'm pretty stuck. How do I get rid of these fractions to get a whole #
2+1+1/4x+1/3x+1/2x=x

Let's start working it together.

The first thing to do in a word problem is identify the unknown number, assign a letter to represent that unknown letter, and to write down briefly what that letter means.

What are we trying to find? What is the unknown? It is the original number of cookies.

x = the original number of cookies. Make sure to write this down so you never forget what x stands for.

The second step is to express the conditions of the problem in math language

How many cookies did Amanda eat?

How many were left after that?

How many of those that were left did Beth eat?

So how many were left after that?

How many of those did Christine eat?

So how many were left after that?

How many of those did Daniel eat.

How many were left after that.

The third step is to set up an equation now that everything is expressed in math speak.

So the cookies left + those Daniel ate + those Christine ate + those Beth ate + those Amanda ate = the original cookies.

What equation do you get when you put that into math speak?

Do you know how to solve that equation?
 
You can't do the problem with subtraction? Like so
X-1/2-1/3-1/4-1=2 <--- in reverse

2,1 and 1/2x are correct; NOT 1/3x and 1/4x.
Beth took 1/3 of WHAT WAS LEFT after Amanda, not 1/3 of original x.
Christine took 1/4 of WHAT WAS LEFT after Amanda and Beth, not 1/4 of original x.

However, I see that you don't know how to add 1/2 + 1/3 + 1/4;
then you're not ready for this problem; you need classroom help.
 
This is a tricky problem. As I said in my first post, it helps to write things down STEP by STEP.

\(\displaystyle x = \text{original number of cookies.}\)

\(\displaystyle \dfrac{1}{2} * x = \dfrac{x}{2} = \text{number of cookies Amanda ate.}\)

\(\displaystyle x - \dfrac{x}{2} = \dfrac{2x - x}{2} = \dfrac{x}{2}\text{number of cookies left by very greedy Amanda.}\)

\(\displaystyle \dfrac{1}{3} * \dfrac{x}{2} = \dfrac{x}{6} \text{one third of remainder gobbled by Beth.}\)

\(\displaystyle x - \dfrac{x}{2} - \dfrac{x}{6}= \dfrac{6x - 3x - x}{6} = \dfrac{2x}{6} = \dfrac{x}{3} = \text{number left after Amanda and Beth pigged out.}\)

OK How many did Christine take?

This seems overly complicated.

\(\displaystyle x * \dfrac{1}{2} * \dfrac{2}{3} * \dfrac{3}{4} -1 = 2\)
Solve for x and done.
 
Okay. I got x( original # of cookies)=12
3/4*2/3*1/2-1=2
Added 1 to the 2 and got 3 and crossed cancelled
(4)1/4x=3(4)
X=12

This seems overly complicated.

\(\displaystyle x * \dfrac{1}{2} * \dfrac{2}{3} * \dfrac{3}{4} -1 = 2\)
Solve for x and done.
 
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