Year 10 Interactive Maths - Second Edition

Problem Solving Unit

Problem 12.1  Age

Nicole is x years old.

a.  What will Nicole's age be in 2 years time?
b.  What was Nicole's age 5 years ago?
c.  State an expression, y, for Nicole's age 5 years ago times her age in 2 years time?
d.  If the value of y is 60, determine Nicole's age.

Problem 12.2  Algebraic Expression

Write an expression for the shaded area in the following diagrams:

a.

b.

Problem 12.3  Rumpus Room

Anna has a rumpus room with side-length x metres.

a.  Determine the area of the rumpus room in terms of x.

b.  Anna plans to extend the rumpus room by 5 metres in both directions to build a larger room.
     Express the area of the enlarged rumpus room in terms of x.

c.  She wishes to replace a square table with a new table whose length is 1 metre longer and
     whose width is 1 metre shorter. Determine the area of the top surface of the new table in
     terms of y, the side-length of the square table.

d.  If the side-length of the original rumpus room was 8 m, calculate:

1. the original floor area of the rumpus room
2. the floor area of the rumpus room after the 5 m extension has been completed
3. the proportion of floor area covered by the new table
4. the unoccupied floor area of the rumpus room after moving the new table into the room.