Percentages

Hong Kong

Stage 1 - Stage 3

Lesson

As we discussed in earlier chapter, people earn money in different ways . However, the most common sources of income people receive are wages and salaries. Let's start by defining these terms.

A **wage** is an amount paid to an employee at a certain rate. It may be calculated as a fixed task based amount, or at an hourly rate, or based on the quantity of work done (e.g. piecemeal work). So if you are paid per hour, your wage will increase the more hours you work.

In contrast, a **salary** is a fixed income that is based on a fixed number of working hours. People normally sign a contract with an agreed salary amount before they start working with a company. An employee may receive a weekly, fortnightly or monthly salary. The employee will receive the same amount of income each time period, regardless of whether they work more or less hours, as it is thought this will be averaged out.

A salary is normally written as an annual amount. However, it can be helpful to calculate how much money you'll receive each week, to help you set a budget for your spending. Similarly, you may want to work out how much money you will earn in a year based on the amount you get paid fortnightly. So let's look at some examples of how to solve questions involving salaries and wages.

Remember

- There are $52$52 weeks in a year.
- There are $2$2 weeks in a fortnight.
- There are $26$26 fortnights in a year.

Note

- It is more accurate to say that there are $52.18$52.18 weeks in a year, however in order to make calculations easier we will often just use $52$52
- Similarly, it is more accurate to say that there are $26.09$26.09 fortnights in a year.

Beth worked for $281$281 days in the year, with an average of $7$7 hours a day. For $62%$62% of those hours, she was paid $\$15$$15 per hour, and for the rest she was paid $\$25$$25 per hour.

**A)** For how many hours was she paid $\$15$$15 per hour? Give your answer to $1$1 decimal place.

**Think:** How many hours does she work in a year?

**Do:**

$281\times7=1967$281×7=1967 hours that she works in a year

$1967\times62%=1219.5$1967×62%=1219.5 hours

**B)** For how many hours was she paid $\$25$$25 per hour? Give your answer to $1$1 decimal place.

**Think: **She was earning $\$15$$15 for 1219.5 hours, and $\$25$$25 for the rest of the year.

**Do:** $1967-1219.5=747.5$1967−1219.5=747.5 hours

**C)** What was her total income for the year (to the nearest cent)?

$1219.5\times15$1219.5×15 | $=$= | $\$18292.50$$18292.50 |

$747.5\times25$747.5×25 | $=$= | $\$18687.50$$18687.50 |

Total | ||

$18292.50+18687.50$18292.50+18687.50 | $=$= | $\$36980$$36980 |

**D)** What was her average weekly income for the year (to the nearest cent)?

**Think:** There are $52$52 weeks in a year.

**Do:** $36980\div52=\$711.15$36980÷52=$711.15

Han earned $\$53030$$53030 in one year, and worked an average of $25$25 hours per week.

What hourly wage did he earn, to the nearest cent?

How much would his annual salary have to increase by for his equivalent hourly wage to increase by $\$4$$4?

Han's annual salary is $\$32630$$32630. Calculate his fortnightly pay after receiving a $5$5% pay rise. Write your answer correct to two decimal places.