Valerie has just had a big win at the lottery. How did she win?

Question

    Valerie has just had a big win at the lottery. She spends 4/5 of her money on a large house. She spends ¾ of her remaining money on a luxury yacht. She spends 2/3 of her remaining money on a trip into space. She gives the remaining $50,000 to charity. How did she win?

 

Answer 1

Let the total amount Valerie won be x.

She spent 4x/5 on large house.

She spent (3/4)(x - 4x/5)  or 3x/20 in luxury yacht.

She spent (2/3)(x - 4x/5 -3x/20) or x/30 in a trip to space.

She spent the remaining $50000 to charity.

So, x - (4x/5 +3x/20 + x/30 + 50000) =0

or x = $30,00,000

So she won $30,00,000

Answer 2

We don’t know how she won but we can work out how much she won.

Let $W be her winnings, then she spent ⅘W on a house, leaving ⅕W.

She spent ¾(⅕W)=3W/20 on a yacht, leaving ¼(⅕W)=W/20. She spent ⅔W/20=W/30 on her space trip, leaving ⅓W/20=W/60=50000.

So she won 60×50000=$3,000,000 ($3M).