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A originally  contains  =  1 / ( 1+3) (720)  =   (1/4) ( 720)  =  180

B + C  =  540

C  =  540  -  B

And   (4/9) 180  =  80  were given away  from  jar A....so it  now contains  100 sweets

And  B now contains  B  - 30

So  we know  that

100 /  ( B - 30)  = 1 /2         (cross-multiply)

200  =  B  - 30

So B originally  contained   230

And  C  originally  contained   540  -  230  =   310

And 60  of these were  given away and  50  were  added

So C  finally  contains   310  - 60 + 50  =  300 

In  the end, each  had     144/3  =    48  erasers

So   Charlie   had  24  erasers  before   getting  24  from  Bill

And   Bill   must  have  had    ( 48  + 24)  =   72  erasers  before  he gave  some to  Charlie

So.....Bill  must have  had  36  erasers  to  start out

Then   Alan must  have started out  with     48 +  36  =  84  erasers

Proof

Alan  starts with 84  and gives away  36  =   he  has 48  in the end

Bill   starts  with 36  gets 36  from Alan and  gives away  24 =  36 + 36 - 24  =   he  has  48 in the end

Charlie  starts out  with  24  and   ends up  with   twice this =  48

Hi Guest,

We can use ratios to solve this problem.

3000 / 120,000 is 1 / 40

So the ratio is 1 : 40

Now the problem asks for house assessed at 160,000

We solve:

160,000 / 40 = 4000

The tax for a house assessed at 160,000 is $4000.00

Hi Guest,

There are 10 Caltech student

There are two choices, either Chipotle or Panda Express

If all 10 go to C or PE, then it's 1

Next, 1 go to C, and 9 go to PE, it is 10

Continue doing that until you reach 5, then add 1 - 5 result up and multiply by two.

Or...

You could do 2^10 = 1024

Hi Guest,

Total is 3m

Climb 1/4x, then -  1/10x

3 = 1/4x - 1/10x

10/40 - 4/40 = 6/40 = 3/20x

3/20x = 3

x = 20

It would take 20 days for snail to get out of well.

See https://web2.0calc.com/questions/question-on-polynomial

Each  day.....the snail   gains      (1/4   -1/10)m    = (.25 - .10),  =   .15m

So.....the  number of days  to  reach   the  top  =   3/.15  =   20 days

So....the  snail gets out  of the  well  on the 21st   day.....!!!!

Hi Guest,

Ratio for price of orange to price of apple is 2 : 3

Can buy 42 oranges

42 : x

So....

42 * 2/3 = 28

He can buy 28 apples

You can't register?

See https://web2.0calc.com/questions/coordinates_112

med in ingredients = med in final solution

x = 20 % cc       amount of med  =   .20 x

(10-x) = 5% cc  amount of med  =   .05 (10-x)        summed they equal   .095 (10)

.20x      +    .05(10-x)       =   .095 (10)         solve for 'x' = the cc of 20%   

                                                                                          then 5 % cc = 10 - x

Thanks Heureka,    

Note that my answer is the same as Heureka's    

In triangle ABC, show

\(CA^2+CB^2=2CM^2+\frac{AB^2}{2}\)

Consider the triangle as I have drawn it and using Cosine rule.

\(a^2=d^2+x^2-2\;d\:x\;cos(180-Q)\\ a^2=d^2+x^2+2\;d\:x\;cos(Q)\qquad\qquad (1)\\~\\ b^2=d^2+x^2-2\;d\:x\;cos(Q)\qquad\qquad (2)\\ add\\ a^2+b^2=2d^2+2x^2\\ \text{Substituting original notation}\\ CB^2+CA^2=2(\frac{AB}{2})^2+2CM^2\\ CA^2+CB^2=2CM^2+2(\frac{AB^2}{4})\\ CA^2+CB^2=2CM^2+\frac{AB^2}{2}\\\)

If Maxi leaves 30 minutes before Pippa Maxi has traveled 20km

130-20=110km

110/80=\(1\frac{3}{8}\) 

\(1\frac{3}{8}\)*40=55

55+20=75km

Lets solvie this:

\(6x^2-31x+42=0\)

\(\frac{-\left(-31\right)\pm \sqrt{\left(-31\right)^2-4\cdot \:6\cdot \:42}}{2\cdot \:6}\)

\(\frac{-\left(-31\right)\pm \sqrt{47}i}{2\cdot \:6}\)

separate: \(x_1=\frac{-\left(-31\right)+\sqrt{47}i}{2\cdot \:6},\:x_2=\frac{-\left(-31\right)-\sqrt{47}i}{2\cdot \:6}\)

\(x=\frac{31}{12}+\frac{\sqrt{47}}{12}i,\:x=\frac{31}{12}-\frac{\sqrt{47}}{12}i\)

okay, so do you understand what Alan has told you?

Thanks Alan :)

Thanx , Heureka !        See answer below....turns out I entered it incorrectly in WA after all.... (transcribed as 'z'  instead of '2z' .... D'Oh!)

Happy birthday Cal. :)))

I hope you have a great day today and eats lots and lots of cake. 

=^._.^=

Melody, webcalc wasnt letting me submit a message on computer so i came on mobile... thank you so much for the bday wishes and it warms my heart that you remembered this day even after so much time passed since we talked. Thank you so much for being the best friend ever to me, ily so much thank you so much ❤

Ive dmd you with more, hope you read it.

♡ c

not allowed to :/

Using the ratios, we can find that z = 24, y = 16, x = 12, and w = 15.

\(x + y + w \over w\) = \(12 + 16 + 15 \over 15\) = \(43 \over 15\)

Hello jleung,

set whole pizza as x

day 1 she eats 1/2x

day 2 she eats 1/3(1/2x), which is 1/6x

day 3 she eats 1/4(1/3x), which is 1/12x

day 4 she eats 1/5(1/4x) which is 1/20x

Total eaten over 4 days: (1/2+1/6+1/12+1/20)x = 4/5x

Answer = left over = 1/5 of the whole pizza

The 'tags' button on the bottom right has a drop-down menu.  Off-topic is in there.

1 g/cm³ = ....  kg/^m³

Hello Guest!

\( \dfrac{1g}{cm^3}\ {\color{black} \cdot \ \dfrac{kg}{1000g} \cdot \dfrac{1\ 000\ 000cm^3}{m^3} }=\dfrac{1000kg}{m^3} \)

  !

Hi Guest,

A pentagon has a sum of interior angle 540 degrees.

Since it is a pentagon, it has five sides.

So....

We divide 540 (total) by 5

540 / 5 = 108 degrees

Measure of each interior angle of the polygon = 108 degrees