Question

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?

Answer 1

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

Answer 2

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.