Math worksheet with a word problem involving fractions and a lottery win.

Let’s solve this step by step, working backwards from the $50,000 he gave to charity.

We know:
- After spending on house, yacht, and space trip, he had $50,000 left.
- He spent ⅔ of his remaining money on the space trip → so the $50,000 is what was left after that.
- That means $50,000 = ⅓ of the money he had before the space trip.
- So before the space trip, he had:
$50,000 × 3 = $150,000

Now, before the space trip, he had $150,000 — which was what remained after buying the yacht.

He spent ¾ of his remaining money on the yacht → so the $150,000 is ¼ of what he had before buying the yacht.
- So before the yacht, he had:
$150,000 × 4 = $600,000

Before the yacht, he had $600,000 — which was what remained after buying the house.

He spent ⅖ of his total winnings on the house → so the $600,000 is ³⁄₅ of his original winnings.
- Let’s call his total winnings “W”.
- Then:
³⁄₅ × W = $600,000
→ W = $600,000 (³⁄₅)
→ W = $600,000 × (⁵⁄₃)
→ W = ($600,000 × 5) ÷ 3
→ W = $3,000,000 ÷ 3
→ W = $1,000,000

✔ Let’s double-check:

Start with $1,000,000

→ Spent ⅖ on house:
⅖ × 1,000,000 = $400,000
Remaining: $600,000 ✔️

→ Spent ¾ of remaining on yacht:
¾ × 600,000 = $450,000
Remaining: $150,000 ✔️

→ Spent of remaining on space trip:
⅔ × 150,000 = $100,000
Remaining: $50,000 ✔️ → given to charity.

Perfect match!

Final Answer:
$1,000,000