Economic information: a table, a chart and a formula

Finance and economics, grade 10 (3 units) Lesson 1 of 15Learning

Economic information: a table, a chart and a formula

A price table

Economic information comes in three main forms: a table, a chart and a formula. From each of them you can draw conclusions and make decisions.

This is the price list of a local gym:

Option	Price
A single entry	40 ₪
A card of 10 entries, for one month	300 ₪
A monthly membership, any number of entries	220 ₪

The example below works out what 5 entries a month cost and what 6 cost, and picks the cheapest option:

5 single entries: $\displaystyle {5\times40}={200}$ ₪ – less than the membership, 220 ₪.
6 single entries: $\displaystyle {6\times40}={240}$ ₪ – more than the membership.

A conclusion from the table

Three conclusions follow from the calculation:

Up to 5 entries a month – pay for each entry.
From 6 entries a month – the monthly membership is cheaper.
The card is never the cheapest: the membership costs less, 220 ₪ against 300 ₪, and gives more entries.

A chart of expenses

A bar chart shows at a glance which expense is large and which is small. These are the Levi family’s monthly expenses:

The largest expense: housing, 4500 ₪.
All the expenses together: $\displaystyle {4500+3000+1500+1000+800+1200}={12000}$ ₪.
Food’s share of all the expenses: $\displaystyle {\frac{3000}{12000}}={\frac{1}{4}}={25\%}$ .
Housing’s share: $\displaystyle {\frac{4500}{12000}}={37.5\%}$ – more than a third of the expenses.

The formula of a plan

A formula describes a price that depends on a quantity. Renting a bike costs a 15 ₪ rental fee and 6 ₪ for every hour. If $\displaystyle x$ is the number of hours and $\displaystyle y$ the price in shekels:

y=15+6x

3 hours: we substitute $\displaystyle {x}={3}$ and get $\displaystyle {y}={15+6\cdot3}={33}$ ₪.
You have 50 ₪, and you pay for whole hours: 5 hours cost $\displaystyle {15+6\cdot5}={45}$ ₪, and 6 hours cost $\displaystyle {15+6\cdot6}={51}$ ₪. You can rent the bike for 5 hours at most.

Three forms of information

Each form suits a different question:

A table – the exact numbers, to work out and compare.
A chart – a picture of the amounts, to see quickly what is large and what is small.
A formula – one rule that gives the price for any quantity, once you substitute it.

Exercise 1

At the town’s swimming pool a single entry costs 35 ₪.
A monthly membership, any number of entries, costs 180 ₪.

a

What do 4 single entries a month cost?

/ – 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

b

From how many entries a month is the membership worth buying?
Work out the price of a few numbers of entries, and explain.

/ – 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

Exercise 2

Noa works after school.
These are her expenses in one month:

a

How much did Noa spend this month in all?

/ – 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

b

What percent of her expenses is going out?

/ – 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

c

On which two expenses did Noa spend the same amount?

Exercise 3

A delivery company charges 20 ₪ for every delivery and 4 ₪ for every kilometre.
The price of a delivery in shekels is $\displaystyle {y}={20+4x}$ , where $\displaystyle x$ is the number of kilometres.

a

What does a delivery over 7 km cost?

/ – 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

b

A delivery cost 56 ₪.
Over how many kilometres was it sent?

Exercise 4

Dana wants to train at the gym of the price list above 12 times a month.
What is the cheapest way for her to pay?
How much cheaper is it than the next cheapest way?

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

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
$\displaystyle \frac{n+1}{2}$