I have a word problem-algebra, please help?

Question

Sally has a box of donuts.
She gives 1/2 of the total to her mom and another 1/2.
She gives 1/2 of what's left to her aunt and another 1/2.
She gives 1/2 of what's left to her sister and another 1/2.
She has 1/4 of a dozen left over.

How many donuts did she start with and how many did each person get?

Please show me the algebra equation you used to get this answer.

Thank you so much

Answer 1

Let x = no. of doughnuts

Her mom got x/2 + 1/2
No. of doughnuts left = x - [x/2 + 1/2] = [x -1]1/2

Her aunt got {[x-1]1/2}1/2 + 1/2 = [x-1]1/4 + 1/2
No. of doughnuts left = [x-1]1/2 - [x-1]1/4 -1/2
= [x-3]1/4

Her sister got {[x-3]1/4}1/2 + 1/2 = [x-3]1/8 + 1/2
No. of doughnuts left = [x-3]1/4 - [x-3]1/8 - 1/2
= [x-7]1/8 = 12/4
= x-7=24
x = 31 doughnuts


Her mom got 31/2 + 1/2 = 16
No. of doughnuts left = 31-16 =15

Her aunt got 15/2 + 1/2 = 8
No. of doughnuts left = 15 - 8= 7

Her sister go 7/2 +1/2 = 4
No. of doughnuts left = 7- 4
= 3 or 1/4 of 12

If you get cross-eyed going through all this, I don't blame you. You just need to be patient and apply some simple arithmetic. The equations are the ones that might give you some problems if you are not careful in solving them.

Answer 2

What do all of the "and another 1/2" mean? It doesn't make grammatical sense. "And another 1/2" of what? Another 1/2 of a single donut?

I'm gonna guess that that is some sort of typo. Either way, the way I would approach this is start from the end and work backwards. If she ends up with 1/4 of a dozen, that's 3 donuts.

She gave that amount to her sister, twice that to her aunt, and 4 times that to her mom. And she started off with twice what she gave her mom:

2 x 4 x 3 = 24

Go back through and double-check:

She starts out with 24, gives 12 to her mom.
She's now got 12, gives 6 to her aunt.
She's now got 6, gives 3 to her sister.
She's left with 3. Check.

Answer 3

of what i understood

total: t

mom's share: c = t/2 + 1/2

aunt's share: b = c/2 + 1/2 or b = (t/2+ 1/2)/2 + 1/2 = (t+3)/4

sister's share: a = b/2 + 1/2 or a = ((t+3)/4)/2 + 1/2 = (t+7)/8

1/4 dozen left over: 1/4 * 12 = 3

t = 3 + a + b + c replacing a, b and c

t = 3 + (t+7)/8 + (t+3)/4 + (t+1)/2

t = 3 * 8/8 + (t+7)/8 + 2*(t+3)/8 + 4*(t+1)/8

8t = 24 + t + 7 + 2t + 6 + 4t + 4

t = 41

she had a total of 41 donuts

mom had (solve c) 21

aunt (solve b) 11

sister (solve a) 6

Answer 4

starting with x donuts
She gives her mom x/2 and another 1/2 of the remaining x/2
He remains with x/4

She gives her aunt 1/2 of x/4 plus another 1/2 of the remaining x/8

she gives her sister 1/2 of the remaining x/16 plus another 1/2 of the remaining x/32.
She is left with x/64

Now x/64 =3 (i.e 1/4 of 12)

Therefore x =64*3

=192

Answer 5

Okay here is what i have.
For first give away, you have (x/2)-(1/2).
Then next give away, you have ((x/2)-(1/2)) - ((x/4)-(1/4)) - (1/2) = (x/4)-(3/4).
Then on last give away, you have ((x/4)-(3/4))-((x/8)-(3/8))-1/2 = (x/8)-(3/8)-(1/2) = (x/8)-(7/8).
And this should equal 3, so (x/8)-(7/8) = 3, so x=31.

SO, he orignallly had 31,
then he gave 16 to his mother,
then he gave 8 to his aunt,
then 4 to his sister.

Answer 6

left over donuts 1/4 * 12 = 3
consider the num of donuts she started be = X
mom gets = X/2
aunt gets 1/2 of wat ur mom got = X/4
sis gets 1/2 of wat ur aunt has got = X/8
therefore total num of donuts = 3 + X/2 + X/4 + X/8 = X
X =24 + 7X / 8
therefore , 8X = 24 + 7X 8X - 7X = 24
therefore , x=24 mom = 12 ,aunt = 6 ,sis = 3 ,urself = 3

Answer 7

she had 2 dozen

Answer 8

Is this homework? Try it urself. I am bad at math