I need help with this math problem, I don't need the answer, just the thought process?

Question

There is this math problem, (and I'm sure it's more simple than I think it is) but I haven't done math in a long time. The thing is, my group has already solved the answer, the answer is 12. But if someone would explain the process to me, that would help!

The person in my group just did the problem without us and told us the answer, and went over it so fast, I didn't get it. I hate it because I'm never gonna have a chance to LEARN while that person keeps doing that!!!

Anyway here's the math problem:

There was a jar of cookies on the table. Amanda was hungry because she hadn't had breakfast, so she ate HALF of the cokies. Then Beth came along and noticed the cookies. She 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 by and took A COOKIE to munch on. Even looked at the cookie jar and saw there were TWO COOKIES LEFT. How many cookies were in the jar to begin with?

The person in the group said the answer was 12 and the class was dismissed. I didn't even have a chance to learn how they got that answer.

I figured the best way to go is go backwards.. and start by adding the remaining 2 cookies with the 1 that daniel ate. But can someone explain step by step the rest of the process? It'll help me learn a lot.. thank you..

Answer 1

You are correct; you should work backwards.

Evan saw the last two cookies --> 2

Daniel ate one cookie, add that back in --> 3

Christine ate 1/4, so 3/4 of the cookies would remain

Let C be the number of cookies before Christine ate 1/4.

C - 1/4C = 3

3/4C = 3

C = 3 * 4/3

C = 4

So Christine started with 4 cookies (eating 1/4 leaves 3).

Beth ate 1/3, so 2/3 of the cookies remaining would be 4 cookies.

Let B be the number of cookies before Beth ate 1/3.

B - 1/3B = 4

2/3B = 4

B = 4 * 3/2

B = 6

So Beth started with 6 cookies (eating 1/3 leaves 4).

Amanda ate 1/2, so 1/2 of the cookies remaining would be 6 cookies.

You can use the same algebra as before.

A = 12

So Amanda started with 12 cookies (eatine 1/2 leaves 6)

Note:  You can also solve this going forward if you like.

Let X be the number of cookies at the beginning.

Amanda eats 1/2.  The remainder is 1/2X

Beth eats 1/3 of what is left, leaving a remainder of 2/3(1/2X) = 1/3X

Christine eats 1/4 of what is left, leaving a remainder of 3/4(1/3X) = 1/4X

Daniel eats one cookie --> 1/4X - 1

Evan notices that there are 2 cookies left, so equate that to 2:

1/4X - 1 = 2

1/4X = 3

X = 3 * 4

X = 12

Answer:

There were 12 cookies to begin with.