Year 10 Interactive Maths - Second Edition

Problem Solving

• distance, speed and time
• area of a paddock or path
• projectiles
• construction of bridges
• logos

The following approach may be useful to solve and model word problems.

• Draw a diagram if necessary and let the unknown quantity be x or some other suitable pronumeral.
• Using the given information, write an equation in terms of x and solve it.
• Check the reasonableness of the solution and state the answer in words.

Example 11

A cyclist takes (x + 3) hours to travel a distance of 108 kilometres when cycling at x kilometres per hour. Find:
a.  the value of x
b.  the time take to complete the journey

Solution:

Example 12

A swimming pool 17 m by 15 m is surrounded by a concrete path, as shown in the following diagram.

Solution:

Example 13

Solution:

So, the width of the base is 3 cm.    

Check:

Example 14

The number of square metres in a square room's floor area exceeds the number of metres in the room's perimeter by 60. Find the side-length of the room.

Solution:

Check:

Study Another Topic in Chapter 12: Quadratic Equations

[ Quadratic Equations ] [ Equations Involving Factorisation ] [ Use of Substitution ] [ Quadratic Equations Containing Fractions ] [ Use of a Square Root ] [ Use of the Difference of Two Squares ] [ The Quadratic Formula ] [ Problem Solving ] [ Problem Solving Unit ] [ Symbols ] [ Index ]