Let’s solve this step by step, working
backwards from the $50,000 he gave to charity — since that’s the final amount left after all his spending.
---
Step 1: Understand the spending order
Bertie spends money in this order:
1. Spends
⅖ of his
original winnings on a house → so
⅗ remains.
2. Spends
¾ of the
remaining money (after house) on a yacht → so
¼ of that remainder is left.
3. Spends
⅔ of the
new remaining money (after yacht) on a space trip → so
⅓ of that remainder is left.
4. That final leftover =
$50,000, which he gives to charity.
---
Step 2: Work backwards
Let’s call the
final amount before charity =
Amount after space trip =
A
We know:
> He spent ⅔ of the money *before* the space trip, so
⅓ remained, and that ⅓ = $50,000.
So:
>
⅓ × (money before space trip) = $50,000
→ Multiply both sides by 3:
>
Money before space trip = $50,000 × 3 = $150,000
---
Step 3: Before the yacht purchase
Before the space trip, he had $150,000. That was what was left
after buying the yacht.
He spent
¾ of the money *before* the yacht on the yacht, so
¼ remained → and that ¼ = $150,000.
So:
>
¼ × (money before yacht) = $150,000
→ Multiply both sides by 4:
>
Money before yacht = $150,000 × 4 = $600,000
---
Step 4: Before the house purchase
Before the yacht, he had $600,000. That was what was left
after buying the house.
He spent
⅖ of his
original winnings on the house, so
⅗ remained → and that ⅗ = $600,000.
So:
>
⅗ × (original winnings) = $600,000
→ Multiply both sides by 5/3 to solve for original winnings:
>
Original winnings = $600,000 × (5/3) = $1,000,000
---
✔ Final Answer: Bertie won $1,000,000
---
Let’s double-check forward:
- Original:
$1,000,000
- House: ⅖ × 1,000,000 =
$400,000 → Remaining:
$600,000
- Yacht: ¾ × 600,000 =
$450,000 → Remaining:
$150,000
- Space trip: ⅔ × 150,000 =
$100,000 → Remaining:
$50,000
- Charity:
$50,000 ✔️
Perfect!
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💡 Hint Tip: Fraction Strips
If you’re using fraction strips (visual aids):
- Start with a strip representing the whole amount ($1M).
- Fold or shade ⅖ for the house → ⅗ left.
- Take that ⅗ piece and fold it into 4 parts → take away 3 parts (¾ spent on yacht), leave 1 part (¼ of ⅗ = ⅕ of total? Wait — better to think step-by-step as above).
- Actually, fraction strips are great for visualizing each step’s “remaining” portion — but since the fractions are applied to *different wholes*, it’s easier to use algebra or work backwards as we did.
---
✔ Answer: Bertie won $1,000,000.
Parent Tip: Review the logic above to help your child master the concept of hard math word problems.
