https://file.aiquickdraw.com/mathbot/file/17297723213364q7nhcj2.jpg

Let’s define the amounts that each person gets using variables:

- Let Polly's share be \( x \).
- Since Andy gets twice as much as Polly, Andy’s share will be \( 2x \).
- Phoebe gets three times as much as Andy, so Phoebe’s share will be \( 3 \times 2x = 6x \).

Now, the total amount they share is £270, so we can set up the following equation:

\[
x + 2x + 6x = 270
\]

Simplify the equation:

\[
9x = 270
\]

Solve for \( x \):

\[
x = \frac{270}{9} = 30
\]

So:
- Polly gets £30.
- Andy gets \( 2x = 2 \times 30 = 60 \) pounds.
- Phoebe gets \( 6x = 6 \times 30 = 180 \) pounds.

### Final amounts:
- Polly: £30
- Andy: £60
- Phoebe: £180

Would you like further details on the solution or have any questions?

Here are 5 related questions to expand on this concept:
1. How would the solution change if Phoebe only received twice as much as Andy instead of three times?
2. What if the total amount shared was £540 but with the same ratio between Polly, Andy, and Phoebe?
3. How can you check if the total of the shares adds up correctly?
4. What is the percentage of the total amount that each person receives?
5. If Polly received £50 instead of £30, how would that affect Andy and Phoebe's amounts?

**Tip:** Always define variables clearly when setting up a problem with ratios or relationships like this, as it simplifies solving the equations.

Phoebe, Andy, and Polly share £270. Phoebe gets three times as much as Andy, who gets twice as much as Polly. Work out how much they each get.

Learn how to solve a ratio-based word problem where Phoebe, Andy, and Polly share £270. Using algebraic equations, we determine how much each person receives when Phoebe gets three times as much as Andy, and Andy gets twice as much as Polly. Suitable for Grades 6-8.

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