Slimesewer

{Drew played 11/12 of the games, Will played 4 games.}

1 - 11/12 = 1/12

4 / 1/12 = 4 * 12 = 48

48 * 11/12 = 44

Let Chase had jellybeans = x

Peter had jellybeans = 5/6 of x

                                  = 5x/6

Chase gave jellybeans to Peter = 1/2 of x

                                               = x/2

Now Chase had jellybeans = x - x/2

                                           = x/2

Now Peter had jellybeans = 5x/6 + x/2

According to problem

                5x/6 + x/2 = x/2 + 55

                5x/5 + x/2 - x/2 = 55

                     5x/6 = 55

                          x = (55 * 6)/5

                          x = 66

Chase had jellybeans at first = 66

Let us assume Sam had x nuggets & fishballs at first.

He had 30 (nuggets + fishballs)

He exchanged every 1 nuggets for 2 fishballs.

He had (30 - x) nuggets at first.

Exchanging all of his nuggets will give him (30 - x) * 2 fishballs.

                                                                   = 60 - 2x fishballs.

The total number of fishballs he had now (60 - 2x + x) [after exchanging all the nuggets] = 60 - x

By the problem,

60 - x = 48

=> x = 60 - 48

=> x = 12

Sam had 12 fishballs at first.

Let weekly pocket money of Tim = x

and Sam's weekly pocket money = y

According to question,

            x = y + 13.50 => y = x - 13.50

Tim spends = 5/11 * x ---- (1)

Sam spends = 5/11x + 17.70 ---- (2)

Total saving of Tim = x - 5x/11 = 6x/11

Sam's saving = 1/2 * 6x/11

Sam spends = Sam's weekly pocket money 

                               -- Sam's saving

5x/11 + 17.70 = y - (6x/(2 * 11))

5x/11 + 17.70 = (x - 13.50) - (6x/22)

5x/11 + 17.70 = x - 6x/22 - 13.50

5x/11 - x + 6x/22 = - 13.50 - 17.70

(10x - 22x + 6x)/22 = -31.20

6x/22 = 31.20

x = (31.20 * 22)/6

x = 114.4

Sam's weekly spend = 5x/11 + 17.70

                              = (5 * 114.4)/11 + 17.70

                              = 52 + 17.70

                              = $69.70

Let No. of $2 gift packs = 16x

      No. of $5 gift packs = 9x

      No. of $10 gift packs = 7x

1/8 of $2 gift packs = 1/8 * 16x = 2x.

Total gift packs = 16x + 9x + 7x

                         = 32x

Total sold gift packs = 1/8 of $2 and 34 of $5

                                = (8x + 34)

     remaining gift packs = Total - Sold

                                      = 32x - (8x + 34)

                                      = (30x - 34)

Remaining gift packs -----> $2 ---> 14x

                                           $5 ---> 9x - 34

                                           $10 ---> 7x

        Value of $2 gift box = (14x * 2) = $28x

        Value of $5 gift box = 5(9x - 34) = $(45x - 170)

        Value of $10 gift box = 10(7x) = $70x

      Total remaining value = $(28x + 45x - 170 + 70x)

                     1975            = (143x - 170) dollars

                         2145 = 143x

                      => x = 15

   No. of $10 gift packs = 7x

                                     = 7 * 15

   No. of $10 gift packs = 105

=> Let assume the number of bags in shop (A) be x and in shop (B) be y

Now, According to question :-

        x = 180 + y ------ (1)

Also (180 + y) * 1/5 were transferred to shop (B)

So, y + (180 + y) * 1/5 = 24 + 4/5 (180 + y)

=> y + 36 + y/5 = 24 + 144 + 4/5y

=> y = y/5 - 4/5y = 144 + 24 - 36

v> 2/5y = 132 => y = 330

[Total No. of Bags in Shop (B) = 330]

Let the number of fruits be x,

the number of pears be y the number of oranges be z.

y:z = 2:7

                           => y = 2/9 (3/5x)
y + z = x (1 - 2/5)     z = 7/9 (3/5x)

Apples : 2/5x

Pears: 2/15x

Oranges: 7/15x

2/5x: 2/15x: 7/15x = 6:2:7

Suppose the full price cost of a bench is $x.

then x + 2 * (1 - 25%)x + 2 = (1 - 50%)x = 385

        x + 2 * 0.75x + 2 * 0.50x = 385

                 x + 1.5x + x = 385

                               3.5x = 385

                                    x = 110 dollars

Let number of micro boxes be m

                       standard boxes be s

                       large boxes be l

           m : s = 3 : 1

                    = 3x and x

     m + s + l = 444

   or, 3x + x + l = 444

    or, 4x + l = 444 .... (1)

     60% micro and 25% large boxes are sold.

          40/100m + s + 75/100l = 285

        or, 40/100 * 3x + x + 75l/100 = 285

        or, (200x + 75l)/100 = 285

        or, 220x + 75l = 285 * 100

        or, 44x + 15l = 5700 .... (2)

Multiplying, eqn. (1) by 15 and subtracting eqn (2) from

              eqn (1) we get 

                60x + 15 l = 6660

                44x + 15 l = 5700

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

               16x        =    960

                   x = 60

Putting value of x in eqn (1) -> 240 + l = 444

                                                or, l = 204

      Micro boxes = 30 * 6 = 180

      Standard boxes = 60

      Large boxes = 204

(a) D = 6 * 2 + (10 - 6)

         = 12 + 4 

         = 16

      r = 1/2D = 16 * 1/2 = 8

(b) S_z = π ((10²) - π - (8²))

          = π(100 - 64) = 113.097 cm² ≈ 113.10 cm²

(c) S_y = π * 6² = 36π

     S_x  = π * 8² - π * 6² = 64π - 36π = 28π

       Y/X = SY/SX = 36π/28π = 9/7