Three students, Ailin, David and Rashaad, received an innovation award for their ground breaking work on scientific discovery. They have decided to split the award as follows: Ailin receives $10,000 plus 1/5 of what then remains; David receives $16,000 plus 1/4 of what then remains, and Rashaad then receives the rest, which is $18,000. How much is the original monetary award? Which student receives the most money?

Now, Ailin receives $10000 plus [tex]\frac{1}{5}[/tex] of what then remains, and David receives $16000 plus [tex]\frac{1}{4}[/tex] of what then remains, and finally Rashaad receives $18000.

So,from the conditions given above we can write

[tex][10000 + \frac{x - 10000}{5}] + [16000 + (x - 10000 - \frac{x - 10000}{5}) \times \frac{1}{4}] + 18000 = x[/tex]

⇒ [tex]10000 + \frac{x}{5} - 2000 + 16000 + \frac{x}{4} - 2500 - \frac{x}{20} + 500 + 18000 = x[/tex]

⇒ [tex](\frac{x}{5} + \frac{x}{4} - \frac{x}{20}) + 40000 = x[/tex]

⇒ [tex]\frac{2}{5} x + 40000 = x[/tex]

⇒ [tex]\frac{3}{5} x = 40000[/tex]

⇒ x = $66666.67

Therefore, Ailin receives [tex][10000 + \frac{66666.67 - 10000}{5}][/tex]

= $21333.34

And David receives [tex][16000 + (66666.67 - 10000 - \frac{66666.67 - 10000}{5}) \times \frac{1}{4}][/tex]

= $27333.33

The original award is of $66666.67 and David receives the most money. (Answer)