apsiganocj

Question was answered here https://web2.0calc.com/questions/ratio_39

ratio of the distance is equal to radius of hour and minute hands. So ratio is 6:8 = 3=4

Ok I answered

Suppose Nate's total money is $x and the cost of 1 curry puff is $y.

Since the cost of 1 apple pie is twice the cost of a curry puff.

Therefore the cost of 1 apple pie is $2y.

Now the cost of 6 curry puffs and 13 apple pies is $(6y + 26y) = $32y.

Since Nate spent 1/3 of his money on 6 curry puffs and 13 apple pies.

Therefore           

    32y = \({x \over 3}{}{}\)
 ⇒ x = 96y  .............. (1)

Now the remaining money is x - x/3 = 2x/3.

  3/4 of the remaining money is 3/4 * 2x/3 = x/2.

Since he bought more apple pies with 3/4 of the remaining money (^$\({x\over 2}{}{}\)) and he paid a total of $92.50 for all the apple pies.

Therefore

    26y + x/2 = 92.50

⇒ 26y + 96y/2 = 92.50    using equation (1)

⇒ 74y = 92.50 

⇒ 2y = 92.50/37

⇒ 2y = 2. 50

So Nate pay $2.50 for 1 apple pie.

Let Bryan had x apples.

He put 1/3 of the apples and another 4 into basket A, i.e.

\( ({x \over 3}+4){}{}\)apples in basket A.

So, remaining apples are 

x - (x/3 + 4)=\(( {2x \over 3}- 4).{}{}\)

Now, he put1/3 of the remaining apples and another 3 into basket B, i.e. 

1/3 (2x/3 - 4) + 3 = (2x/9 - 4/3 + 3) = (2x/9 + 5/3)

apples in basket B.

This time remaining apples are 

(2x/4 - 4) - (2x/9 + 5/3) = (4x/9 - 17/3).

Now, he put 1/3 of the rest and another 3 into basket C, i.e.

1/3 (4x/9 - 17/3) + 3 = (4x/27 + 10/9) apples in basket C.

So, the remaining apples are

(4x/9 - 17/3) - (4x/27 + 10/9) = (8x/27 - 61/9).

But in the end, he had 3 apples left for himself, i.e.

(8x/27 - 61/9) = 3

⇒ (8x/27) = 3 + 61/9 =88/9

⇒ x = 88/9 * 27/8 = 33

So,

33 apples he have at first.

Then the number of marbles Albert has is given by;

n_A = x - 152 

Now when Bernard give away 2/3^rd of his marble, he will be left with ;

(1 - 2/3)x = x/3

-marbles.

And when Alfred give away 3/4^th of his marbles, he will be left with ;

(1 - 3/4)(x + 152) = \({ 1\over 4}{}{}\) (x + 152)

-marbles.

Now it is given that at this stage Bernard will have 9 more marbles than Alfred. i e ;

1/3x = 1/4 (x + 152)+9

Now solving the above equation for x as follows;

1/3x=1/4(x + 152)+9

\({x\over 3}\frac{}{}\)\(= {(x +152) + 9⋅4 \over 4}\frac{}{}\)

      =\( {x +188 \over 4}{}{}\)

x ⋅ 4 = 3 (x + 188)

         = 3x + 3 ⋅ 188

      4x=3x + 564

4x - 3x = 564

         x = 564

Therefore initial number of marbles Bernard had was 564 marbles. Therefore number of marbles Alfred had is given by;

x + 152=564 + 152

            =716

Therefore Alfred had 716 marbles. And he gave away 3/4^th of his marbles. ie;

\({3 \over 4}{}{}\)⋅ 716 = 537

Therefore Alfred gave away 537 marbles 

And the number of marbles left with him is given by;

716−537=179

Therefore Alfred is left with 179 marbles.

given data in

1/3rd of the pens are red.

number of black pens was 11 pens then 1/2 of the red pens.

There were total 284              blue pens.

To find number of black pens.

Assume that there are x red pen, y black pens, z blue pens, then

                      x = 1/3 (x + y + z)

                      z = 284    and         y+11=1/2x

=>        3x = x + y + z   ;  z = 284  ;   2y+22=x

            2x-y=284            x-2y=22

            2(2y+22)-y=284

               4y + 44 - y = 284

                 3y = 240

                   y = 80       x = 2 (80) + 22 = q82

                                    x = 182

Thus there were total 80 black pens.

               Let:

Before: 

                Philip's money = x dollars

                                                       ]

                Mark's money = x dollars 

After: Accoriding to question:

          Philip's money = (x - 50)  dollars

          Mark's  money = ( x - \(xx {1 \over 3}{}{}\)) = \( {2x \over 3}{}{}\)dollars
 

                According to question:                 
                   x-50/2x/3 = 5/4

                   3 (x-50)/2x = 5/4

                   3x-150/2x 5/4

                  12x - 600 = 10x

                   12x - 10x = 600

                              2x = 600

                                x = 300 dollars

So,

        Philip had remaining money = x - 50 = 300 - 50 = $250

Given : 

Intially ratio of pencil to eraser in a box = 3:4

After adding 12 pencils and removing 15 erasers it became 1:1. 

To find : 

How many eraser in the box ?

Given that the ratio of pencil to eraser is 3 : 4 .

If there is initially x pencils and y erasers ,

So, we can write

x/y = 3/4 

Or y = 4x/3

And if we add 12 more pencils and remove 15 erasers then the ratio will be 1 : 1,

So, we can write

(x + 12) / (y - 15) = 1/1

x  + 12 = y - 15

Now, put the value of y

x + 12 = 4x/3 - 15

4x/3 - x = 15 + 12.

x/3 = 27

x = 81.

Now y will be

y = 4x/3

y = 108

But it is the Intial values of x and y.

The number of erasers at the end will be

= y - 15

= 108 - 15

= 93

The number of erasers in the box at the end is 93.