Hourly pay and overtime

Finance and economics, grade 10 (3 units) Lesson 11 of 15Learning

Hourly pay and overtime

Pay by the hour

In a job paid by the hour you get a fixed sum for every hour of work – the hourly wage.
Noa works in a café and gets 40 ₪ an hour.
On Friday she worked 6 hours.

Her pay for that day: $\displaystyle {40\cdot6}={240}$ ₪.
Every extra hour adds 40 ₪: the pay is a linear model, and the hourly wage is its slope.

When $\displaystyle w$ is the hourly wage and $\displaystyle h$ the number of hours:

\displaystyle S=w\cdot h

A week’s pay

Last week Noa worked by this table:

Day	Sunday	Monday	Tuesday	Wednesday	Thursday
Hours	5	4	6	0	5

The hours in all: $\displaystyle {5+4+6+0+5}={20}$ .
The week’s pay: $\displaystyle {40\cdot20}={800}$ ₪.

You could also work out each day’s pay and add them up – the same sum, by a longer calculation.

Exercise 1

Work out the pay.

35 ₪ an hour, 7 hours

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

42.5 ₪ an hour, 12 hours

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

38 ₪ an hour, a week of 4, 6, 3 and 5 hours

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

Overtime

Overtime is the hours worked beyond a normal working day, and they are paid more than the hourly wage.
In this course’s examples a normal working day is 8 hours, and the rule is:

the first two overtime hours of a day – 125% of the hourly wage;
from the third overtime hour of a day – 150% of the hourly wage.

When $\displaystyle w$ is the hourly wage, an overtime hour is paid:

\displaystyle 1.25\cdot w

\displaystyle 1.5\cdot w

Overtime is counted for each day apart: a day of 10 hours and a day of 6 hours are 2 overtime hours, not two “normal” days of 8.

Example: a day of 11 hours

Dan gets 48 ₪ an hour.
One day he worked 11 hours.

In the example below we split the 11 hours into three parts and work out the pay for each:

8 normal hours: $\displaystyle {8\cdot48}={384}$ ₪.
2 overtime hours at 125%: $\displaystyle {2\cdot1.25\cdot48}={2\cdot60}={120}$ ₪.
1 overtime hour at 150%: $\displaystyle {1\cdot1.5\cdot48}={72}$ ₪.

384+120+72=576

Dan earned 576 ₪ that day. Without the overtime extra he would have got $\displaystyle {11\cdot48}={528}$ ₪.

Exercise 2

Work out the pay for the working day.
A normal day is 8 hours.

44 ₪ an hour, 10 hours

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

40 ₪ an hour, 12 hours

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

Exercise 3

Uri gets 50 ₪ an hour.
A normal day is 8 hours.
These are the hours he worked in one week:

Day	Sunday	Monday	Tuesday	Wednesday	Thursday
Hours	8	10	9	8	11

How much did Uri earn that week?

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

The hours needed for a sum

When you know how much you want to earn, an equation gives the number of hours.
Noa wants to earn 1000 ₪ in normal hours, at 40 ₪ an hour.

Call the number of hours $\displaystyle x$ : $\displaystyle {40x}={1000}$ .
Divide both sides by 40: $\displaystyle {x}={25}$ .

Noa needs to work 25 hours.

Exercise 4

Maya gets 45 ₪ an hour, with no overtime.
She wants to earn 1800 ₪ for a trip.
Write an equation and solve it: how many hours does she need to work?
Maya works 10 hours a week. How many weeks will it take her?

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

Exercise 5

Ido has two job offers:
Offer A – 46 ₪ an hour, and overtime by the rule (a normal day is 8 hours).
Offer B – 48 ₪ for every hour, with no overtime extra.
Which offer pays more for a day of 8 hours?
And for a day of 10 hours?

Formulas: finance and economics, grade 10 (3 units)

Open as a page

Buying and selling

The unit price – $\displaystyle P$ the price of the pack, $\displaystyle n$ the number of units in it (grams, litres, items)
$\displaystyle u=\frac{P}{n}$
A $\displaystyle p\%$ discount – $\displaystyle a$ the price before the discount, $\displaystyle b$ the price after it
$\displaystyle b$ $\displaystyle =$ $\displaystyle (100\%-p\%)\cdot a$
A price with 18% VAT – $\displaystyle a$ the price without VAT, $\displaystyle b$ the price with VAT
$\displaystyle b$ $\displaystyle =$ $\displaystyle 1.18\cdot a$

A linear model

The total cost – $\displaystyle x$ the number of units, $\displaystyle m$ the cost per unit (the slope), $\displaystyle b$ the fixed cost
$\displaystyle y=mx+b$
The cost per unit from two points $\displaystyle (x_1,y_1)$ , $\displaystyle (x_2,y_2)$ on the line
$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$
Two plans cost the same – where their two lines meet
$\displaystyle m_1x+b_1$ $\displaystyle =$ $\displaystyle m_2x+b_2$

Profit and loss

The total cost – $\displaystyle F$ the fixed costs, $\displaystyle c$ the cost of one unit, $\displaystyle x$ the number of units
$\displaystyle C=F+c\cdot x$
The revenue – $\displaystyle s$ the selling price of one unit
$\displaystyle R=s\cdot x$
The profit – the revenue minus the cost (a negative profit is a loss)
$\displaystyle P=R-C$
The profit percent – out of the cost
$\displaystyle r\%=\frac{P}{C}$
The break-even point – the revenue equals the cost
$\displaystyle s\cdot x$ $\displaystyle =$ $\displaystyle F+c\cdot x$

Wages

Pay – $\displaystyle w$ the hourly wage, $\displaystyle h$ the number of hours
$\displaystyle S=w\cdot h$
The pay for an overtime hour, in the first two overtime hours of a day
$\displaystyle 1.25\cdot w$
The pay for an overtime hour, from the third overtime hour of a day
$\displaystyle 1.5\cdot w$
Net pay – $\displaystyle G$ the gross pay, $\displaystyle D$ the deductions
$\displaystyle N=G-D$

Measures of centre

The mean of $\displaystyle n$ values
$\displaystyle \bar{x}=\frac{x_1+x_2+\dots+x_n}{n}$
The mean from a frequency table – $\displaystyle f_i$ the frequency of the value $\displaystyle x_i$
$\displaystyle \bar{x}=\frac{x_1f_1+x_2f_2+\dots+x_kf_k}{f_1+f_2+\dots+f_k}$
The place of the median in an ordered list of $\displaystyle n$ values
$\displaystyle \frac{n+1}{2}$