Year 9 Interactive Maths - Second Edition

Problem Solving

Example 5

The denominator of a certain fraction is 1 more than the numerator, and the sum of the numerator and the denominator is 7.  Find the fraction.

Solution:

Substituting  y = x + 1 in (2) gives:

Substituting x = 3 in (1) gives:

Example 6

The length of a rectangular orchard is 40 m more than the width, and the perimeter is 200 m. Find the length and width.  Hence determine the area of the orchard.

Solution:

Let the length and width of the rectangular orchard be l m and w m respectively.  Then:

Substituting l = w + 40 in (2) gives:

Substituting w = 30 in (1) gives:

So, the length and width are 70 m and 30 m respectively.