Question 10300: Mary bought some donuts. She gave 1/2 her donuts and 1/2 a donut to her mom. Then she gave away 1/2 her remaining donuts and 1/2 a donut to her aunt. Then she gave 1/2 of her remaining donuts and 1/2 a donut to her sister, Kathy. This left her with 1/4 of a dozen donuts. How many doughnuts had she bought?
Found 2 solutions by rapaljer, mathmaven53:
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Let's work this one backwards:
Mary ends up with 3 donuts after giving half of them and a half a donut to her sister Kathy. This means that before giving donuts to her sister Kathy, Mary must have had 7 donuts (of the 7 donuts, she gave half of them--3 1/2--plus a half, which would be 4 donuts to her sister, leaving her with 3 donuts for herself!)
Now, this means that she ended up with 7 donuts after giving half of them plus a half donut to her aunt. By the same thinking, she must have had 15 donuts before giving 8 donuts to her aunt (7 1/2 + 1/2), leaving 7 for herself.
So, if she ended up with 15 donuts after giving half plus a half a donut to her mother, she must have started out with 31 donuts.
Now check it by seeing if it works:
Mary started with 31 donuts (half would be 15 1/2, + 1/2 means that she gave 16 to her mother), which leaves her with 15. She gave 7 1/2 + 1/2 or 8 to her aunt, leaving her with 7 donuts. She gave 3 1/2 + 1/2 or 4 to her sister, leavning her with 3 donuts or 1/4 of a dozen.
Do you think there is a math formula for this? Did you notice that at each step of the problem, each time she had donuts left, it was 1 less than a power of 2? She started with 31 ( 32 -1), went down to 15 (16-1), then to 7 (8-1), and 3 (4-1). Interesting problem. Probably some high powered math here!!
R^2 at SCC
Answer by mathmaven53(29)  (Show Source):
You can put this solution on YOUR website! Try 31 donuts
Gives away half of them and 1/2 donut to mom This is 16 donuts gone
leaving 15 donuts. Gives half of remainder and 1/2 donut to aunt. This is 8 donuts gone leaving 7 donuts. Gives half of this and 1/2 donut to sister.
This is 4 donuts gone leaving 3 donuts which is 1/4 of a dozen.
I used an equation and perhaps I can redo this solution later and show how I got the equation.
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