Analysis of Mathematics Curriculum 1

Social ArithmeticPresented By :

1.Eko Widyaningsih ( 4101413102 )2.Khamida Nuriana ( 4101413161 )

Semarang State University2013/2014

Buying Price, Selling Price,

Profit, and Loss

Trades involve the sellers and the buyers. The sellers deliver goods to the buyers, while the buyers pay some money as a compensation for the goods received.

To have the goods to sell, the sellers buy from the manufacturers, wholesalers, or other parties. The price of goods the factories, the wholesalers or other parties charge is called the buying price, while the amount of money received by the sellers from selling the goods is called the selling price.

In a trade, there are two possible outcomes a seller may face, i.e. :

1. The seller earns a profit, or

2. The seller suffers a loss.

Total Value and Value per Unit

To find out the total value, we must know the value per unit first.

To find out the value per unit, we must know the total value first.

Total Value = Number of unit x Value per unit

Percentage of Profit and Loss

Profit and Loss

If selling price is higher than buying price, it makes profit.

If selling price is lower than buying price, it makes loss.

Profit = Selling Price – Buying Price

Loss = Buying Price – Selling Price

There are two ways to determine profit and loss, by amount and percentage.

Profit Percentage

Loss Percentage

Discount, Gross, Tare,

and Net

Discount and RebateA price reduction is called discount, while rebate means cutting price for the things you bought in large amount, for example if you bought one dozen of the books. Discount and rebate has the same calculation.

Gross, Tare, and NetGross is the weight of the pack and its

content. Net is the weight of the content (without the pack). The difference between gross and net weights is called tare. In the other word, tare is the weight of the pack only. Tare = Gross

- NetTare can be expressed as percentage of gross, that is

TaxPaying tax is an obligation to every citizen by which they submit some of

their wealth to their country according to the rules set by the government, without direct returns

from the country. The money collected by taxation is used to

promote public welfare.

Employees of private companies or government officials are imposed the tax on their taxable income known as the income tax.

When we buy from dealers, wholesalers, department stores or other sellers, the price of the goods we buy includes another kind of tax called a value added tax (VAT).

Income tax = percentage of income tax x annual income

VAT = percentage of VAT x selling price

Note :1.Income tax leads to a reduction in someone’s income

2.Value added tax (VAT) leads to an increase in the buying price

ExampleA worker receive Rp1,500,000.00 as a salary and imposed by tax in 15%.Determine his salary after imposed by tax.

SolutionThe salary is Rp1,500,000.00Tax that must be paid by worker is 15% x Rp1,500,000.00 x Rp1,500,000.00 Rp225,000.00So, the salary to the worker after imposed by tax is Rp1,500,000.00 – Rp225,000.00Rp1,275,000.00

Saving Interest

How to calculate saving

interest ?

The way to calculate saving interest is formulated as :

I = Saving interestT = Time to save the capitalP = Percentage of interestC = Capital (amount of saved money)

I = T x P x C

If T is stated in month, so the formula should be :

If T is stated in day, so the formula should be :

Interest rate always refers to annual interest, unless stated otherwise.

Review1.

2.

3.

4.

Profit = Selling Price – Buying Price

Loss = Buying Price – Selling Price

Total Value = Number of unit x Value per unit

5.

6.

7.

8.

Tare = Gross - Net

I = T x P x C

Profit Percentage

Loss Percentage

VAT = percentage of VAT x selling price

Income tax = percentage of income tax x annual income

9.

10.

Problem

A seller buys 25 kg of oats A at Rp6,000.00/kg and 15 kg of oats B at Rp4,000.00/kg. Then, both of them are mixed. How much the selling price of oat per kg in order to get profit at 4%?

1

SolutionXA= Rp6,000.00 ; fA = 25XB= Rp4,000.00 ; fB = 15X = ? ; fAB= 40

X = X = X = X = X = Rp5,250.00

Buying price after they are mixed is Rp5,250.00/kg

Profit = 4% x buying price = 4% x Rp5,250.00 = Rp210.00

Selling Price = Buying Price + Profit

= Rp5,250.00 + Rp210.00

= Rp5,460.00/kg

Problem

A book costs Rp3,000.00. Anita’s money is worth only to buy 10 books. If the book price decrease into Rp2,500.00, how many books Anita can buy? 2

SolutionIf one book prices is h, and Anita’s money only enough to buy 10 books, we can write that Anita’s money is 10 x h = 10hIf the book prices decrease into Rp2,500.00, the number of books that Anita can buy is

Problem

A seller bought 100 breads at a price of Rp600,000.00. Later, 40 breads were sold at a price of Rp7,000.00 each, 52 breads were sold at a price of Rp6,000.00 each, and the rest were broken. What was the amount of loss the seller suffered?

3

SolutionBuying price = Rp600,000.00Selling price = (40 x Rp7,000.00) + (52 x Rp6,000.00) = Rp280,000.00 + Rp312,000.00

= Rp592,000.00Loss = Buying price – Selling price

= Rp600,000.00 – Rp592,000.00 = Rp8,000.00

So, the amount of loss the seller suffered is Rp8,000.00

Problem

Ami buys barbie doll for Rp370,000.00. If she get 15% discount, how much is the discount? How much is the selling price of the barbie doll after getting a discount? 4

Solution

Ami get 15% discount for Rp370,000.00Thus, the discount is

Therefore, the selling price of barbie doll after getting the discount is

Rp370,000.00 – Rp55,500.00 = Rp314,500.00

Problem

Mr. Anjas borrows Rp7,800,000.00 at cooperation with interest rate 10% per year.

If the loan must be paid within a period of 8 months, how much money must be paid by Mr. Anjas each month?

5

SolutionThe money that borrowed by Mr. Anjas = Rp7,800,000.00 The interest rate = 10% per yearThe amount of interest for 8 months is

The installment which must be paid each month is

Problem

Interest rate of deposit in bank is 8% per year. If money at Rp750,000.00 deposited in the bank. How much the money after 15 months?

6

SolutionInterest rate = 8% per year Deposited money = Rp750,000.00Amount of interest for 15 months is

Amount of money after 15 months is Rp750,000.00 + Rp75,000.00

Rp825,000.00

ProblemUncle Arno earns Rp950,000.00 a month and the tax-exempted income is Rp360,000.00.

If the income tax is imposed at a rate of 10%, what is the net salary Uncle Arno earns?

7

SolutionThe amount of taxable income = Rp950,000.00 – Rp360,000.00 = Rp590,000.00The amount of income tax = 10% x taxable

income

= Rp59,000.00

Uncle Arno’s net salary is

Rp950,000.00 – Rp59,000.00

Rp891,000.00

Problem

Isyna buys a radio set at a price of Rp180,000.00 with a 10% value added tax (VAT).

How much must Isyna pay for the radio?

8

Solution

Value added tax = 10% x Rp180,000.00

= Rp18,000.00

Isyna has to pay Rp180,000.00 + Rp18,000.00 =

Rp198,000.00

Problem

A seller buys 5 sacks of rice each having a gross weight of 72 kg and a tare of 1%.

How much a seller must pay if the price per kg rice is Rp4,000.00? 9

SolutionGross weight = 5 x 72 kg

= 360 kg

Net weight = 360 kg – 3.6 kg = 356.40 kg

A seller must pay = 356.40 x Rp4,000.00 = Rp1,425,600.00

ProblemWahyu and Ganang have the same salary in 2001. At January 1, 2002, Wahyu’s salary increase 15% while Ganang’s salary increase 10%. Exactly a year later, Ganang’s salary increase 15% and Wahyu’s salary increase 10%. Who is salary in 2003 is bigger? 10

SolutionUse double interest pattern to answer this problem.Let Wahyu and Ganang’s salary in 2001 = MWahyu’s salary calculation is

M (100% + 15%) + (10%)(M(100%+15%))1.15M + 0.1 (1.15M)1.15M (1 + 0.1)(1.15M) (1.1)M (1.15) (1.1)

Ganang’s salary calculation is

M (100% + 10%) + (15%)(M(100%+10%))

(1.1)M + (0.15)(1.1M)

1.1M (1 + 0.15)

1.1M (1.15)

M (1.15) (1.1)

Now, their salary is same.

ProblemA city transport has the payment rule

as follows :

On the way up each passenger must pay Rp600.00, after 4 km first have to pay Rp1,400.00, and every take the next 2 km must pay Rp150.00 and pay Rp100.00 after 1 km.

Oei ride the city transport as far as 21 km. What is the minimum money to be paid Oei for the city transport service? 11

SolutionOn the way up = Rp600.00When 4 km first = Rp1,400.00When the next 2 km = 8 x Rp150.00 When the next 2 km = Rp1,200.00The remaining 1 km last = Rp100.00

So, the minimum money to be paid Oei isRp600.00 + Rp1,400.00 + Rp1,200.00 +

Rp100Rp3,300.00

Thank You