"Bill at 1/3 of the cookies in the cookie jar. Maria ate 1/2 of what was left. Then Sidney ate 2 cookies. Now 4 are left. How many were in the jar to start with?"
Any help would be greatly appreciated seeing as I have no clue of where to begin!
"Bill at 1/3 of the cookies in the cookie jar. Maria ate 1/2 of what was left. Then Sidney ate 2 cookies. Now 4 are left. How many were in the jar to start with?"
Any help would be greatly appreciated seeing as I have no clue of where to begin!
Hello, pleasehelpme12345!
Let $\displaystyle N$ = number of cookies in the jar.
Bill ate $\displaystyle {\color{blue}\tfrac{1}{3}}$ of the cookies.
He ate $\displaystyle \tfrac{1}{3}N$ cookies.
There were $\displaystyle \tfrac{2}{3}N$ cookies left.
Maria ate $\displaystyle {\color{blue}\tfrac{1}{2}}$ of what was left.
She ate $\displaystyle \tfrac{1}{2}\left(\tfrac{2}{3}N\right) = \tfrac{1}{3}N$ cookies.
There were $\displaystyle \tfrac{1}{3}N$ cookies left.
Then Sidney ate 2 cookies.
There were: $\displaystyle \tfrac{1}{3}N - 2$ cookies left.
Now 4 cookies are left.
There is our equation! . $\displaystyle \hdots\quad \tfrac{1}{3}N - 2 \;=\;4$
Now solve for $\displaystyle N.$
To help solve future problems, here's a tip. When you read it, try writing out the equation in a mix of english / math.
Janice ate 1/2 of the cokoies in the jar. John ate 7/8 of the remaining. the dog ate 1. there were none left. How many cookies were there? (I just made up the numbers)
Janice ate 1/2 the cookies in the jar ==> 1/2 * jar
john ate 7/8 of the remaining = john ate 7/8 * (jar * (remaining from what john ate = 1/2) ) = 7/8 * (1/2 * jar)
the dog ate 1 = the dog ate 1....so 1.
there were none left means there are none in the bowl which means all cookies were eaten.
the sum of all of what is eaten is what was originally there...so just sum it up! substitute x for jar if you want...but u get the idea.
Hope it helped.