Slimesewer

324 / 162 = 2

105 * 5 2^2 = 105 * 4 = 420

The population of bacteria will have 420

Tom has 9 balls

and also n/2 + n/4 balls 

so n/2 + n/4 = 9

   (2n + n)/4 = 9

   2n + n = 36

    3n = 36

      n = 12

Jack has n balls

      n = 12

        12 balls

Jack made 2 1/3 dozen chocolate cookies,

1 dozen peanut cookies

1 1/2 dozen oatmeal cookies.

1 dozen = 12 cookies

Therfore, 2 1/3 * 12 = 7/3 * 12

                                = 84/3

                                = 28 chocolate cookies

                      1 * 12 = 12 peanut cookies

                1 1/2 * 12 = 3/2 * 12

                                = 36/2

                                = 18 oatmeal cookies

Find the greatest common denominator;

2 | 28  12  18

   |-----------------

     14   6   9

He could fill 2 bags with the same 

number of each cookies in each bag.

Peter saved = 12 one dollar bills

After he paid he left with 1/3 of them

         = 1/3 of 12

         = 4 dollar bills

6. $12 start --> $2 left = 5/6th money

          Alexander spent $10 at the

          mall and has $2 left.
5. Jordan spent $24

      he spent less than 1/2 of his money

         24 / (1/3) = 72    72 - 24 = 48

    Jordan spent $24 at the mall

    and has $48 kept.

7. Justin = $24 left   (1/2) yes 11/12 no 1/12 no

    24 / (1/2) = 48

    Justin spent $24 at the mall

    and has $24 left.

2. Benjamin spent $8 (1/12) yes 11/12 no

         8 / (1/12) = 96     96 - 8 = $88

    Benjamin spent $8 at the mall

    and has $88 left.

4. 11/12

    $60 start

   $60 * 11/12 = $55     60 - 55 = $5

    Zachary spent $55 at the mall

    and has $5 left.

Let Tom have = x strawberries

    Peter have =  y straberries

When Tom gave 1/3

      Tom = x - x/3 = 2x/3

      Peter = y + x/3

When Peter gave 1/4

    Peter = (y + x/3)3/4 = 3y/4 + x/4

      Tom = 2x/3 + (y + x/3) 1/3 = 2x/3 + y/4 + x/12

  When Tom gave 1/5

     Tom = (3x/4 + y/4)4/5 = (3x + y)/5
   Peter = ((3y + x)/4) + (3x/4 + y/4)1/5 => (4y + 2x)/5

     Tom =  (3x + y)/5 = 32

             => (1) --- 3x + y + 160

                         3x + y = 160

                    3(x + 2y = 140)

      3x + y = 160

      3x + 6y = 420

-------------------------

      0 - 5y = -260

             y = 52

Peter = (4y + 2x)/5 = 56

=> 4y + 2x = 280 (2)

     2y + x = 140

3x + (52) = 160

3x = 108

x = 36

x + 0.085(x) = 35

   1.085x = 35

   1.085x/1.085 = 35/1.085

            x = 32.26

    --> 32.26 (0.085)

    --> $2.74

Initial tokens = 60

left tokens = 24

used tokens = 60 - 25

                    = 35

% of used tokens = used token/inital tokens * 100

                             = 35/60 * 100

                             = 58.3%

Ans: 58%

We have two conditions 

Let x = the load of your teuck

and y = load of their trucks then

1)  x ≥ y + 800 .... (1)

   4y = the total load of their trucks

(1/5) * 4y = the load of your truck

2)   4/5 * ≤ y .... (2)

Calculations:-

                       x = y + 800 .... (1)

                       x = 5y/4 .... (2)

Put value of (2) in (1) so

              5y/4 = y + 800

         => 5y/4y - y = 800

         => 1/4y = 800

         =>  y = 3200 pounds

then put y = 3200 in (2)

       x = 5/4 (3200)

       x = 4000 pounds

4000 pounds is the greatest load that your truck carry

Let x be the number of paper cranes 

      y be the number of paper stars

(1)  x + y = 516 => x = 516 - y

(2)    2nd day cranes :

              x - 5/6x + 72 = 1/6x + 72

        2nd day stars : 

               y - 2/3y + 84 = 1/3y + 84

          (1/6x + 72)/1/3y + 84 = 3/4

           2/3x + 288 = y + 252

              x + 3/2 (288) = 3/2(y + 262)

              x = 3/2y + 378 - 432

              x = 3/2y - 5$

By comparison x = x

     3/2y - 54 = 516 - y

     3/2y + y = 516 + 54

     5/2y = 570

          y = 228

Amy folded 228 paper stars on the first day.