Review: finance and economics

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

Review: finance and economics

1

These are the prices at the town swimming pool:

Ticket	One entry	A card of 10 entries	A monthly pass
Price (₪)	35	300	220

A card and a pass are for one month only.

a

Tamar swims 6 times a month.
What is cheapest for her?

b

Asaf swims 10 times a month.
What is cheapest for him, and how much does he save compared with single entries?

/ – 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

2

A supermarket sells two bottles of olive oil:
a 750 ml bottle for 30 ₪;
a 1 litre bottle for 38 ₪.

a

Work out the price per litre of the small bottle.

/ – 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

Which bottle is cheaper per litre? By how much?

/ – 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

3

A phone company offers two plans:
Plan A costs 20 ₪ a month plus 0.3 ₪ for every minute of calls.
Plan B costs 0.5 ₪ a minute, with no monthly fee.
On the graph, $\displaystyle x$ is the number of minutes a month and $\displaystyle y$ the price in shekels; plan B is the dashed line.
Mark where the lines meet on the graph.
Solve the equation: for how many minutes a month do the two plans cost the same?
Raz talks about 150 minutes a month. Which plan should he choose?

\displaystyle y=0.3x+20

\displaystyle y=0.5x

4

VAT is 18%.

a

A washing machine costs 850 ₪ without VAT.
How much does it cost with VAT?

/ – 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 plumber’s bill, with VAT, is 590 ₪.
Solve the equation: how much is it without VAT?

5

A coat costs 400 ₪.
At the end of the season it got a 20% discount, and at the till another 10% off the new price.

a

How much does the coat cost in the end?

/ – 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 the original price is the whole discount?

/ – 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

6

A market stall owner bought 40 shirts at 25 ₪ each.
She sold them all, at 40 ₪ each.

a

What is her profit?

/ – 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 is the profit percent, out of the 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

7

A small bakery has 3000 ₪ of fixed costs a month.
Each cake costs 12 ₪ to make, and sells for 27 ₪.

a

Write an equation and solve it: how many cakes must it sell a month to reach the break-even point?

b

Write an equation and solve it: how many cakes must it sell a month to make a profit of 1500 ₪?

8

Gal gets 44 ₪ an hour.
A normal day is 8 hours: the first two overtime hours at 125%, from the third at 150%.
One day Gal worked 11 hours.
How much did he earn that day?

/ – 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

9

Merav’s gross pay is 8000 ₪.
On her pay slip the deductions are 11% of the gross.
What is her net pay?

/ – 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

10

5 flats are offered for rent in a neighbourhood.
This is the monthly rent of each, in shekels:
$\displaystyle 4000, 4300, 4500, 4800, 9400$

a

Work out the mean rent.

/ – 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

Find the median.
A family is looking for a flat in the neighbourhood. Which measure of centre tells it better how much it will pay? 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

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