*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.

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3 years ago