Slimesewer

(1) a 10 cents off coupon, every other box, 2

(2) a pencil, 5

(3) a coupon for a free hamburger, 8

If there are three, that means it's the least common multiple of 2,5, and 8

becuase it's : 40,

So 100 / 40 = 2 ... 20.

So have 2 boxes.

Aaron : Ben

3 : 4

Ben : Calvin

2 : 5

4 : 10

Aaron : Ben : Calvin

3 : 4 : 10

6 : 8 : 20
Calvin has 2 * x badges

Ben has 8x badges

Aaron has 6x badges

from question,

Aaron's badges + 8 = Ben's badges

6x + 8 = 8x

x = 4

20x - 8x = 12x

12 * 4 = 48

48 more badges Calvin have than Ben.

(1) T = 1/3 (C + D)

(2) C = 2/5 (T + D)

(3) T = D - 24

   D - 24 = 1/3 (C + D)

 3D - 72 + C + D

   C = 2D - 72

   C = 2/5 (D - 24 + D)

   C = 2/5 (2D - 24

 2D - 72 = 2/5 (2D - 24)

 5D - 180 = 2D - 24

 3D = 156

 Dave = $52

    T = 52 x 24

 Terry = $28

    C = 2 (52) - 72

 Carl = $32

The present cost = 52 + 28 + 32

                           = $112

2r, = 10 yd

r1 = 5yd

r2 = r1 + 11yd

    = 5 + 11 yd

r2 = 16 yd

Area of Shaded region

          = 3.14r2²- 3.14r1²

          = 3.14 (r2²-r1²)

          = 3.14 (16² - 5²)

          = 3.14 (231)

          = 725.34 yd²

Let x = # of pencils in Box A originally

        x + 480 (80%) = x + 30% x

                  48/0.3 = 0.3x/0.3

                        x = 160

* 160 + 48 = 208

* 208 (1 - 0.75) = 208 (0.25) = 52

* 52 (1 - 0.75) = 52 (0.25) = 13 pencils left

(a) P:5x Q:3x (P = Q = 5x : 3x = 5:3)

per profit = (180 (5x + 3x) - 140 (5x) - 160 (3x))/(140 (5x) + 160 (3x)) * 100%

               = (1440x - 1180x)/1180x * 100%

               = 0.220 * 100%

               = 22% or 22.03%

(b) P:Q = 5:3

    P = 10x, Q = 6x (P:Q = 10x : 6x = 5:3)

    Q = R = 2:5

    Q = 6x, R = 5(3)x = 15x

      (Q : R = 6x : 15 = 6:15 = 2:5)

   => P = Q : R = 10x = 6x = 15x = 10 : 6 : 15

(c) selling price = y

40% = (y (10x + 6x + 15x) - 140 (10x) - 160 (6x) - 256 (15x))/(140 (10x) + 160 (6x) + 256 (15x))

=> 0.4 = (31 * y / 6200x)/6200x

     0.4 = (31y - 6200)/6200 => 31y = 8680, y = $280 per litre

assume x represent the shots on target when same rate was 33 1/3%

total shots: x/33 1/3% = 3x

(x + 1)(/3x + 1) = 0.4

x + 1 = 1.2x + 0.4

0.2x = 0.6

x = 3

y represent times consecutive shots on target must be saved to raise the same rate to 60%

(x + 1 + y)/(3x + 1 + y) = 0.6

(3 + 1 + y)/(3.3 + 1 + y) = 0.6

(4 + y)/(10 + y) = 0.6

4 + y = 6 + 0.6y

0.4y = 2

y = 5

Let x be no. of erasers

      y be no. of stickers

Mark

1/2x

1/2y - 6

1/2y - 6 = 1/5(1/2x)

(y - 12)/2 = x/10

5y - 60 = x

5y - 60 = (3y + 20)

y = 40, x = 140

Susan 

1/2x - 10

1/2y

1/2y = 1/3(1/2x - 10)

3y = x - 20

3y + 20 = x

Susan bought 40 stickers

Area of quarter circle = 1/4πr²

                                  = 1/4 * π * 3² = 7.065 km²
Area of rectangle = Length * width 

                            = 5 * 8 = 40 km²

Area = 1 * 6 = 6 km²

Total area = (7.065 + 40 + 6) km²

                 = 53.065 km²

For rectangle 1st, length(1) = 13 yard, base(1) = 5 yd

For rectangle 2nd, length(2) = 8 yard, base(2) = 4 yd

Area = area of triangle + area of A rectangle = area of 1st rectangle + area of 2nd rectangle

        = 1/2 * base * height + length(1) * base(1) + length(2) * base(2)

        = 1/2 * 3 * 3 + 5 * 13 + 8 * 4 yd²

        = 9/2 + 65 + 32 yd²

        = 4.5 + 65 + 32 yd²

        = 101.5 yd²