Problem Solving

Naturally enough, problem solving is about solving

problems.

method + answer = solution

method + answer = solution

• method – means used to get an answer

• answer – number, quantity or some other entity that the problem is asking for.

• solution – whole process of solving problem, including the method of obtaining an answer and the answer itself.

Four Stages of Problem Solving

1) Understand and explore the problem;

2) Find a strategy;

3) Use the strategy to solve the problem;

4) Look back and reflect on the solution.

Example:

The length of a rectangle is three times more than its width. Its perimeter is 50. solve for its sides.

Solution:

Let x = short sidex + 3 = L

2x + 2(x + 3) = 50 2x + 2x + 6 = 50

4x = 50 – 6 4x = 44 x = 44/4 x = 11

Therefore:

x = 11; shorter side of the rectangle

x + 3 = 14; length of the rectangle

Thus,

2x + 2(x + 3) = 50

2(11) + 2(14) = 50

22 + 28 = 50 √

Example:

The sum of two numbers is 12. The sum of two times the larger number and three times the smaller number is 29. Find the value of two numbers.

Solution:

Let x = larger numberLet 12 – x = smaller number

2x + 3(12 – x) = 29 2x + 36 – 3x = 29

-x = 29 – 36 -x = -7

x = 7; larger number 12 – 7 = 5; smaller number

Proof:

2 x 7 = 14

3 x 5 = 15

14 + 15 = 29 √

ConsumerMathematics

Consumer Mathematics

presents basic math skills used in everyday situations – paying taxes, buying food, banking and investing, and managing a household.

Sales Commissions

• paid to employees or companies that sell merchandise in stores or by calling on costumers.

• meant to motivate sales person to sell more.

• may be paid in addition to a salary or instead of a salary.

• usually in real estate marketing.

Sales Commissions

• generally a percentage of sales price of an item.

• example:

if a person receives a 10% commission on their sales and sells a P15,000.00 worth of merchandise, they would earn P1,500.00

15000 x 0.1 = 1500

Price Discounts

• stores often sell items for a discounted sales price.

• ex:An item originally costs P200.00 may be

discounted by 25%.

200 x .25 = 50

200 – 50 = 150; sales price

Most terms seen for discounted items:

• 50% off

• Save 50%

• Discounted by 50%

Markup

• original cost plus amount of markup

• ex:If the original cost is P400.00 and the markup is

25%, the sales price should be

400 + (400 x 0.25) = 500

100% + 25% = 125%

400 x 1.25 = 500

Amount of Sales Tax

• determined by finding a percentage of the purchase price.

• percentage of tax called tax rate varies between different cities.

• ex:If the sales tax is 6% and a P1,000.00 purchase

is made, the sales tax is

1000 x .06 = 60

Total Price with Sales Tax

• total purchase plus the sales tax

• If the sales tax is 6% and a P1,000.00 purchase is made, the sales tax is

1000 x .06 = 60

1000 + 60 = 1060

Shipping and Handling

• often assessed to cover the packing and postage or shipping charges for getting the item, usually on mail orders.

• there is frequently a minimum charge for small orders. If the order is more than the minimum, a shipping and handling charge is calculated as a percent of the total purchase price.

Shipping and Handling

• ex:If there is a minimum charge of P50.00 on

orders less than P500.00 or 10% of the total order price, and your order is P650.00, the shipping and handling would be

650 x 0.1 = 65

The total cost would be

650 + 65 = 715

Simple Interest

• Interest = Principal x Rate x Time

• ex:If P10,000.00 was borrowed for 2 years at a

10% interest, the interest would be

10000(2)(0.10) = 2000

The total amount that would be due

10000 + 2000 = 12000

Simple Interest

Compound interest is similar but the total amount due at the end of each period is calculated an further interest is charged against both the original principal but also the interest that was earned during that period.

Unit Price of Items

• the cost for each unit.

• the unit price may be calculated to find the cost of a single item when many items are purchased together.

• required if the items are going to be resold or divided among several people with each person paying the fair share of the cost based on how many items they receive.

Cost Based on Unit Price

• may be calculated when the unit cost is known and the quantity that will be purchased is decided.

• ex:If a meal cost P65.00 is served for 100 persons,

the total cost is

100(65) = 6500

Group 1 Reporters

Bengan, Catherine Rose

Castro, Karen Kae

Ebarle, Giff

Flores, Fritz

Isip, Christine

Jalad, Ma. Adela

Nombrado, Lady Dianne