David has two younger sisters, Jane and Sally. Jane is 2 years older than Sally and David is 4 times older than Jane. Sally is z years old. Part A Write two equivalent expressions that represent David's age in terms of Sally's age, z, and explain how the two expressions relate to one another. Part B Which expression is more useful? Why?

Part A:

Given that Sally is z years old and Jane is 2 years older than Sally, then Janes age is given by z + 2.

Given that David is 4 times older than Jane, then Davids age is given by 4 (z + 2)

Therefore, two equivalent expressions that represent David’s age in terms of Sally’s age, z are 4 (z + 2) and 4z + 8.

Part B:

The expression that is more useful is 4z + 8 because it is in a simplified form and given the direct relationship between David's age and Sally's age.

Sally is "z" years old.

We can write the expression "years older than Sally" like this:

2+z

The expression "4 times older than Jane" can be written in maths like this:

4 (2+z)

since Jane is (2+z) years old.

We deduce David’s age in terms of Sally’s age:

8+4z