Ratio Question; 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.

-Please help, no links. Thanks!

*Given

Money of Phoebe            - 3 times as much as Andy

Money of Andy                - 2 times as much as Polly

Total money of Phoebe,  - £270

   Andy and Polly

*Solution

Let

B - Phoebe's money

A - Andy's money

L - Polly's money

1. The money of the Phoebe, Andy, and Polly, when added together would total £270. Thus,

                 B + A + L  = £270                     (EQUATION 1)

2. Phoebe has three times as much money as Andy and this is expressed as

                 B = 3A

3. Andy has twice as much money as Polly and this is expressed as

                 A = 2L                           (EQUATION 2)

4. This means that Phoebe has as much money as Polly,

                B = 3A

                B = 3 x (2L)

                B = 6L                            (EQUATION 3)

This step allows us to eliminate the variables B and A in EQUATION 1 by expressing the equation in terms of Polly's money only.

5. Substituting B with 6L, and A with 2L, EQUATION 1 becomes,

                 6L + 2L + L = £270

                               9L = £270

                                 L = £30

So, Polly has £30.

6. Substituting L into EQUATIONS 2 and 3 would give us the values for Andy's money and Phoebe's money, respectively.

                 A = 2L                          

                 A = 2(£30)

                 A = £60

Andy has £60

                 B = 6L                        

                 B = 6(£30)

                 B = £180

Phoebe has £180

Therefore, Polly's money is £30, Andy's is £60, and Phoebe's is £180.