Question

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?

Answer 1

Answer:

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

Step-by-step explanation:

Let us assume that the total prize money is $x.

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

So,from the conditions given above we can write  

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

⇒ $10000 + \frac{x}{5} - 2000 + 16000 + \frac{x}{4} - 2500 - \frac{x}{20} + 500 + 18000 = x$

⇒ $(\frac{x}{5} + \frac{x}{4} - \frac{x}{20}) + 40000 = x$

⇒ $\frac{2}{5} x + 40000 = x$

⇒ $\frac{3}{5} x = 40000$

⇒ x = $66666.67  

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

= $21333.34

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

= $27333.33

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