Bro took half. Sis took 2 thirds. Mom took 1 half. 5 Cookies left. How many cookies?

Question

This is so hard.

 

Answer 1

To solve this by writing the expressions:

Let x = original number of cookies

 

“Bro took half,” so the number left is now (x-x/2)=x/2

“Sis took 2 thirds,” so the number left is now (x/2) – (2/3)(x/2) = (1/3)(x/2) = x/6

“Mom took half,” so the number left is now (x/6)-(1/2)(x/6) = x/12

 “5 cookies left,” so

      x/12 = 5

      x = 60    [multiply both sides by 12]

 

To check:

  Start with 60 cookies

  "Bro took half"  30 cookies left

  "Sis took 2 thirds"  10 cookies left

  "Mom took half"  5 cookies left

  5 cookies left

Answer 2

If there are five cookies left right after Mom took half of the remaining cookies, then right before Mom took her cookies, there were 5*2 = 10 left.

 

Now we have that there were 10 cookies left right after Sis took two thirds of the remaining cookies. Thus, right before Sis took her cookies, there must have been 10*3 = 30 cookies left.

 

Lastly, we have that there were 30 cookies left right after Bro took half of the remaining cookies. Thus, right before Bro took his cookies, there must have been 30*2=60 cookies.

 

Let me know if you have any questions. I am available for online tutoring! :)