Question

Phoebe, Andy and Polly share £270.

Answer 1

*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.