Year 10 Interactive Maths - Second Edition

## Problem Solving

Linear equations are often used to solve practical problems that have an unknown quantity. We use a suitable pronumeral to represent the unknown quantity, translate the information given in the problem into an equation, and then solve the equation using the skills acquired earlier in this chapter.

#### Example 11

If a number is increased by 8, the result is 25. Find the number.

#### Example 12

If a number is decreased by 4, the result is 29. Find the number.

#### Example 13

If twice a number is equal to 68, find the number.

#### Example 14

If a number is divided by 9, the result is 12. Find the number.

#### Example 15

If three times a number decreased by 5 equals 82, find the number.

#### Example 16

If one-half of a certain number is added to one-third of the same number, the result is 10. Find the number.

##### Solution:

So, the number is 12.

#### Example 17

A rectangular paddock is twice as long as it is wide. If it has a perimeter of 570 m, find its dimensions.