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

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

Explanation:

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

Now, Ailin receives $10000 plus
`(1)/(5)` of what then remains, and David receives $16000 plus
`(1)/(4)` of what then remains, and finally Rashaad receives $18000.

So,from the conditions given above we can write

`[10000 + (x - 10000)/(5)] + [16000 + (x - 10000 - (x - 10000)/(5)) * (1)/(4)] + 18000 = x`

⇒
`10000 + (x)/(5) - 2000 + 16000 + (x)/(4) - 2500 - (x)/(20) + 500 + 18000 = x`

⇒
`((x)/(5) + (x)/(4) - (x)/(20)) + 40000 = x`

⇒
`(2)/(5) x + 40000 = x`

⇒
`(3)/(5) x = 40000`

⇒ x = $66666.67

Therefore, Ailin receives
`[10000 + (66666.67 - 10000)/(5)]`

= $21333.34

And David receives
`[16000 + (66666.67 - 10000 - (66666.67 - 10000)/(5)) * (1)/(4)]`

= $27333.33

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