civonamzuk

...or Dragan 

[DMT] = 13 ¹/₃ square units

This is very simple...

AB = 12

BC = 300/12

BW = BC - CW

∠CBD = tan^-1(12/25)

∠BWZ = tan^-1(12/13)

Now you can solve triangle BQW using the law of sines, and using Heron's formula, you can find the area of this triangle.

btw., [BQW] = 57 square units

XY  must be larger than WX !!! 

Here's why:

15 / 14 ≠ (14-YZ) / 15

If WX = 7, and XY = 14 then we have:

XZ / 7 = 7 / 14

XZ = 7/2

YZ = 14 - 7/2 = 21/2

Angle ETF = 105 degrees

EF = 3 + √3

Angle FTG = 75 degrees

Line segment EG is a diagonal of square EFGH.

(Don't ask me how I've done it.) 

Micah spent half of his money and an additional $324 on television.

Then he spent 1/6 of his remaining money and an additional $55 on a DVD

player. Then he spent 0.4 of his remaining money and an additional $18

on a music player. If he has $168 left, how much was the television?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Television cost = x/2 + 324 = $1086

Correction:

8x / 7(x + 26) = (1/3) / (2/5)         x = 70

Mary baked some pies. She packed 1/3 of the pies in 8 small boxes and 2/5 of

the pies in 7 big boxes. She donated the remaining pies to a charity. Each big

box had 26 more pies than each small box. How many pies were packed in

boxes altogether?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Single small box => x           Single big box => x + 26

8x / (x + 26) = (1/3) / (2/5)         x = 70

Total pies = 1232 

Angle BAC = 150 degrees          (60º + 90º)

Richard spent 2/7 of his money on 4 bags and 4 pencil cases. The cost of a bag

is twice that of a pencil case. With 5/6 of his remaining money, he bought more

pencil cases. How many pencil cases did he buy in all?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Cost of 4 pencil cases = 1/3(2/7) = 2/21    or     4/42

Cost of "more pencil cases" = 5/6(5/7) = 25/42

Proportion:        (4/42) / 4 = (25/42) / x          x = 25

Richard bought 29 pencil cases.