Christmas Pie gone

this is a trick question...you have to read very carefully...

Well,everytime he eats a part from he left,not a part from the whole pie...so the calculus its like this way :

(The pie will start with a hundred "pieces" ,because we have to say in % the answer)

1/5 of 100 = 20 =>100 - 20 = 80.

1/4 of 80 = 20 => 80 - 20 = 60.

1/3 of 60 = 20 => 60 - 20 = 40.

1/2 of 40 = 20 => 40 - 20 = 20. So was left 20% of the pie

Consider the pie as 1 unit.

• When the son ate $\frac{1}{5}$ of it, there is $1 - \frac{1}{5} = \frac{4}{5}$ units remaining.

• When the daughter ate $\frac{1}{4}$ of what was remaining, she didn't eat $\frac{3}{4}$ of it,

hence we have $\frac{4}{5} \times \frac{3}{4} = \frac{3}{5}$ remaining.

• When the wife ate $\frac{1}{3}$ of what was remaining, she didn't eat $\frac{2}{3}$ of it,

hence we have $\frac{3}{5} \times \frac{2}{3} = \frac{2}{5}$ remaining.

• When the dog ate $\frac{1}{2}$ of what was remaining, he didn't eat $\frac{1}{2}$ of it,

hence we have $\frac{2}{5} \times \frac{1}{2} = \frac{1}{5}$ remaining.

• So, at the end, the percentage would be $\frac{1}{5} \times 100 = 20$ %.

That's the answer!

left 20% of pie. Because, at 1am my son ate 1/5 of pie, and left 4/5 pie; at 2am, my daughter ate (1/4)(4/5) and left (3/4)(4/5) = 3/5 of pie; at 3am my wife ate (1/3)(3/5) and left(2/3)(3/5) = 2/5 of pie; at 4am my dog ate (1/2)(2/5) and left (1/2)(2/5) = 1/5 of pie, i.e. 20% pie.

Suppose initially pie was 100%. 1. Son ate 1/5 i.e. 20% so 80% left. 2. Daughter ate 1/4 of 80% i.e. 20% so 60% left. 3. Wife ate 1/3 of 60% i.e. 20% so 40% left. 4. Dog ate 1/2 of 40% i.e. 20% so 20% left.

Hence finally in morning 20% of pie is left.

After 1am, the cake was left 4/5. After 2am, the cake was left 3/4 x 4/5. After 3am, the cake was left 2/3 x 3/4 x 4/5. After 4am, the cake was left 1/2 x 2/3 x 3/4 x 4/5 = 1/5 x 100 = 20%.

We start out with $\frac{100}{100}$ of the pie. The son eats $\frac{1}{5}$ or $\frac{20}{100}$ , leaving $\frac{80}{100}$ . The daughter eats $\frac{1}{4}$ of $\frac{80}{100}$ or $\frac{20}{100}$ , leaving $\frac{60}{100}$ . The wife eats $\frac{1}{3}$ of $\frac{60}{100}$ or $\frac{20}{100}$ , leaving $\frac{40}{100}$ . The dog eats $\frac{1}{2}$ of $\frac{40}{100}$ or $\frac{20}{100}$ , leaving $\frac{20}{100}$ . The answer is $\frac{20}{100}$ , or $20$ percent.

The dumb way to do this is like this: note that the answer is $\frac{4}{5}\times\frac{3}{4}\times\frac{2}{3}\times\frac{1}{2}$ , and simply multiply fractions. The cool, slick way to solve this is by realizing that that just equals $\frac{4!}{5!}$ . All of the terms in the numerator cancel out with terms in the denominator except for 5, thus the answer is $\frac{1}{5}$ or $\boxed{20}$ percent.

Let suppose that we've a pie 100 units in weight (kilos seem to me a little too much ) One fifth of the 100 units has been consumed so we've been left with (100-(100/5))=80 units of pie in weight Going this way we see that 20 units are consumed by each person and thus only 20 units worth of pie remaining for the father !

See to it that you take one-Nth of what is left and not that of the original quantity each time you subtract the consumed amount !

First, you would convert the one fifth into 20% of the pie, so 80% was then left until the daughter ate a quarter of what was left so she ate another 20% of the pie, dropping the percent of the pie left over down to 60%. At 3am the wife ate a third of the 60% which is another 20% lost which drops it down to 40%. At 4am the dog then ate half of what was then left which from the 60-20=40 + the half ate = 20%

let the whole pie be x. now find the remaining when son ate { x - x/5 } = 4x/5. now find remaining after the daughter ate { 4x/5 - (1/4) 4x/5 } that comes out to be 3x/5 . now doing for all others remaining { 3x/5 - (1/3) 3x/5 } =2x/5. remaining after dog ate is { 2x/5 - (1/2) 2x/5 } = x/5 . remaining is now x/5. let % be a so equation is (a/100) x = x/5. a = 20%. answer is 20

1 - (1/5) = (4/5) //after son ate the cake

(4/5) - (4/5)*(1/4) = (3/5) // after daughter ate the cake

(3/5) - (3/5)*(1/3) = (2/5) // after wife ate the cake

(2/5) - (2/5)*(1/2) = (1/5) //after dog ate the cake

((1/5)/1)*100 = 20 // (1/5) is 20 % of 1.

if we say that the pie is a 100% then we take out 1/5 from it then we have 80% then the daughter ate 1/4 of it 1/4 out of 80% then what's left is 60% and the wife ate 1/3 out of 60% then the percentage left is 40% and the dog ate 1/2 then the percentage left is 20%. wasn't hard

After the son eats 1/5, or 20%, of the Christmas cherry pie, there is 80% of it left over. At 2am when the daughter comes, she eats 1/4, or 25%, of what is left.That leaves him with 3/5, or 60% of the pie. At 3am when the wife comes, she eats 1/3 of what is left, and one-third of 60 is 20, so that leaves him with 40% of the pie. After the dog comes and eats 1/2 of what is left of the pie, 20%, he is left with 20% of the Christmas cherry pie.

1. 5/5-1/5=4/5
2. 4/5-(1/4*4/5)=4/5-1/5=3/5
3. 3/5-(1/3*3/5)=3/5-1-5=2/5
4. 2/5-(1/2*2/5)=2/5-1/5=1/5 Answer: 1/5=20%......So the answer is 20

After son ate 1/5th, (1-1/5)=4/5th was left. Daughter ate (1/4 of 4/5)=1/5th of it. Remaining part=(4/5-1/5)=3/5. Wife ate (1/3 of 3/5)=1/5 of the cake. Remaining part=(3/5-1/5)=2/5. Dog ate (1/2 of 2/5)=1/5th of it. Remaining part=(2/5-1/5)=1/5=((1/5)*100)%=20%.

Let the original amount of pie be x.

Now, pie left after eaten by son $=x- \frac{1}{5}x = \frac{5x-x}{5} = \frac{4x}{5}$

Pie left after eaten by daughter $=\frac{4x}{5}-\frac{1}{4}\times \frac{4x}{5} = \frac{4x}{5}-\frac{4x}{20} = \frac{16x-4x}{20} = \frac{12x}{20} =\frac{3x}{5}$

Pie left after eaten by wife $=\frac{3x}{5}-\frac{1}{3}\times \frac{3x}{5} = \frac{3x}{5}-\frac{3x}{15} = \frac{9x-3x}{15} = \frac{6x}{15} = \frac{2x}{5}$

Pie left after eaten by dog $=\frac{2x}{5}-\frac{1}{2}\times \frac{2x}{5} = \frac{2x}{5}-\frac{2x}{10} = \frac{4x-2x}{10} = \frac{2x}{10} = \frac{x}{5}$

Percentage of pie remaining $=(\frac{Remaining}{Total}\times 100) = (\frac{\frac{x}{5}}{x}\times 100) = (\frac{1}{5}\times 100) = \boxed{20}$

total = x; son eat x/5; daughter eat (x-x/5)1/4=x/5; wife eat (x-x/5+x/5)1/3=x/5; dog eat (x-x/5+x/5+x/5)1/2=x/5; remaining food is (x-x/5+x/5+x/5+x/5)=x/5; remaining food percentage is (x/5)/x*100=20%

the whole cherry pie is 100% and divided the cherry pie into 5 pieces and find out percentage for each pieces (100/5=20)each piece has 20% and four pieces are taken by four members and finally one piece is left and its percentage is 20..

It's simple ...

first ... his son ate 1/5 of the pie ... so the remaining of the pie is 4/5 ...

then , he said that his daughter ate 1/4 of the remaining .... remember .. subtracting directly from 4/5 is totally wrong ..the correct one is .. you must find what is the value of the part that been eaten by his daughter .... this would work ..

4/5 x 1/4 = 4/20

the remaining of the pie is

4/5 - 4/20 = 16-4/20 = 12/20

then , his wife ate 1/3 of it .. so the correct way to solve it is ....

12/20 x 1/3 = 12/60 ... this is the part that eaten by his wife ..

the remaining is .... the 12/20 ( remaining that eaten by his daughter ) - 12/60

12/20 - 12/60 = 36 - 12 /60 = 24/60 then ...his dog ate 1/2 of the remaing .... so .... the dog ate ...

24/60 x 1/2 = 24/120

the remaining shoul be .... 24/60 ( the remaining eaten by his wife ) - 24/120

24/60 - 24/120 = 48 -24/120 = 24/120

thus , the percentage of the remaining

24/120 x 100% = 20 %

Suppose the initial is x. So:

at 1 am, the remainder is: $x-x/5= 4x/5$

at 2 am, the remainder is $4x/5- 1/4*4x/5= 3x/5$

at 3 am, the remainder is $3x/5- 1/3 *3x/5= 2x/5$

at 4 am, the remainder is $2x/5- 1/2*2x/5= x/5$

The remainder at the morning is $(x/5)/x *100 percent= 20 percent$

This is a good application level problem of multiplication of fractions. What we need to do is just multiply (4/5).(3/4).(2/3).(1/2) and then convert the answer into percent.

Consider the pie has 10 pieces... Son ate 1/5 of pie.. i.e. 2 peces... left over is 8 pieces... Daughter ate 1/4 of left over pie.... i.e. 2 pieces.... left over is 6 pieces..... Wife ate 1/3 of 6 pieces.... i.e. 2 pieces... left over is 4 pieces.... Dog ate 1/2 of 4 pieces... i.e. 2 pieces... left over is 2 pieces.... Left over pieces converted to percentage is 2/10*100 = 20%

(1-1/5) (1-1/4) (1-1/3) (1-1/2)=1/5=20%

100% - 1/5 is 80%. 80% - 1/4 is 60 % 60% - 1/3} is 40% 40 -1/2 is 20%

FIRST, DIVIDE THE PIE IN FIVE PARTS BECAUSE THE FIRST GIVEN IS 1/5...
WHOLE PIE IS EQUAL TO 100% SO EACH PART OF THE PIE HAS 20%... THE SON ATE 1/5 OF IT SO REMOVE ONE OF THE FIVE PARTS THEN THERE ARE FOUR REMAINING... REMOVE ONE PART AGAIN BECAUSE THE DAUGHTER EAT 1/4 ( ONLY ONE PART HAS REMOVED BECAUSE THERE ARE ONLY FOUR PARTS REMAINING) SO NOW THERE ARE ONLY THREE REMAINING... REMOVE AGAIN ONE PART BECAUSE HIS WIFE EAT 1/3 (ONE OUT OF THREE PARTS REMAINING) SO NOW THERE ARE TWO REMAINING... REMOVE 1/2 OF THE REMAINING BECAUSE HIS DOG ATE IT, SO NOW THERE ARE ONLY ONE PART REMAINING... I ALREADY EXPLAINED THAT ONE PART IS EQUAL TO 20% SO THE PERCENTAGE OF PIE LEFT FOR HIM IS 20%...

Assume x = 10;

x - 0.2x = 10 - 0.2(10) = 8; x = 8

x - 0.25x =8 - 0.25(8) = 6; x = 6

x - (1/3)x =6 - (1/3)(6) = 4 ; x=4

x - 0.5x =4 - 0.5(4) = 2; x=2

x=2/10 * 100% = 20%

(nlife)

1am eaten 1/5 remaining 4/5, 2am eaten 1/4 remaining 3/4, 3am eaten 1/3 remaining 2/3, 4am eaten 1/2 remaining 1/2.

Multiply all remains. 4/5 * 3/4 * 2/3 * 1/2 * 100% = 20%

@ 1 am 1x (1-1/5) = 4/5. <---> @ 2 am 4/5 x ( 1- 1/4) = 3/5 <---> @ 3 am 3/5 x (1-1/3) = 2/5 <---> @ 4 am 2/5 x ( 1 - 1/2) = 1/5 = 20%. Answer : 20

since and 1-1/n= n-1/n, we can think first of a pie as multiple amounts of slices, first it was cut in 5 even slices, then 4 out of 5 slices were cut into 4 more even slices then 2 0 slices were cut into 3 even slices and then finallly, 60 slices were cut into 2 even slices, at each itoration 1 portion was taken out, consequently we can first find how many total slices were left over and then how many all the clices the cake was cut into. (4 3 2)/(5 4 3*2)=24/120,=1/5 of the cace was left, or 20 percent.

Let the whole pie be 1 My son eats =1/5 of 1 So the pie left is =1-1/5 =4/5 My daughter eats =1/4 of 4/5 =1/5 The pie left now is=1-portion of my son ate -portion my daughter ate =1-1/5-1/5 =1-2/5 =3/5 My wife gets=1/3 of 3/5 =1/5
My dog gets =(1-3/5) of 1/2 =1/5

So the pie left is =1-1/4 =1/5

so the percentage is 20%