Ratio and Proportion

Like fractions, ratio and proportion has already been studied in our earlier days. And it is just as important to the real world.  

A ratio is a relationship between two numbers of the same kind like a:b
A proportion is an equation a:b = c:d stating that two ratios are equivalent.

Sample problems:

15ft to 45 ft
Solution:in this problem, get the lowest term of the two numbers which is 15
                =15 is 1 and 45 is 3 so
                =15/45 = 1/3

30 minutes to 2 hours
Solution: convert first the hours into minutes which is 1 hour = 60 minutes
               = 2*60 = 120
               = 30 minutes and 120 minutes, get the lowest term which 30
               = 30 is 1 and 120 is 4
               = 30/60 = 1/4

If 2 ballpen cost 20 php. How many ballpens will she have if he has 320php
Solution: make a proportion formula and represent the second ballpen with x
                 = 2 ballpen                x ballpen
                   -------------     =     --------------
                    20 pesos                 320 pesos
                 = cross multiply
                      2*320 = 640 and 20* x = 20x
                 = 640 = 20x divide the number by 20 (to make the x an individual number)
               
                 = 640    20x   = 32 = x
                    -----   ------
                     20      20
                 = she will have 32 pencils

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Prof. Cris Paner

Fraction

fractions are a common term in elementary days but it is as common to the real world. Although it may not seem to be that used, it is important to relearn this lessons the addition, subtraction, multiplication and division of fractions.

Sample problems:

At a wedding, the girls ate  3 1/2 slices of cake and the boys ate 6 1/2 of sliced cake. How many cakes were eaten at the wedding?
Solution: 3 1/2 + 6 1/2
                  turn the mixed number into improper 2*3+1 = 7/2 and 2*6+1 = 13/2
                  since both are the same denominator just add them
                  ==== 10 slices of cake


Rizza bought 2 1/2 gallons of water and gave 2/4 of the water to the neighbor. How much water is left?
Solution: 2 1/2 - 2/4
                 turn the mixed number into improper 2*2+1 = 5/2
                 find their lcd which is 4, then 4/2*5 = 10/4
                                                                    4/4*2 = 2/4
                 subtract the two number
                 ==== 2 gallons

Ms. Go has a lemonade stand. She used 4/5 bags of lemonade on friday and on saturday, she used 1/2 as many lemonades on friday. How many bags of lemonade did she use on saturday?
Solution: 4/5*1/2
                 in multiplication, just multiply it like normal... 4*1 and 5*2
                  ==== 4/10, simplify then 2/5

1/8 of the original cake is left on the refrigerator. If there are 4 siblings that will share on it. How much cake per sibling will have?
Solution: 1/2 / 4
                 in division it's like multiplication but you will invert the 2nd number so 1/8 * 1/4
                 ====  1/8 cake per sibling

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Prof. Cris Paner

Borrowing and Lending Money

Everyone has supposedly experienced borrowing or lending money, to friends and you yourself borrowed to them. And as you lend them money you sometimes joke to them "hey there's an interest when you give it back to me". Well as a continuation to that it's time to understand how interest really works.

The first thing to do about interest is learning a couple of formulas:
1. I=Prt
2. t=I/Pr
3. r=1/Pt
4. F=P+1
5. F=P+Prt
6. F=P(1+rt)
7. P=F/(1+rt)
8. t+1/r(F/P-1)

where:
I = interest
t = time (expressed in years unless if stated months in the problem)
r = interest rate
P = principal amount
F = final amount

*to change the time from years to months just multiply it by 12 (since there are 12 months) and from months to years is divide it by 12.

Next time someone borrows money from you try to compute the interest as a practice, it might come in handy. The most important thing to remember are the formulas and designating the right number to the right term. 

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sample problem: Find the time in months investing P30,000 at the rate of 12% if the person earns an interest of P459?

SOLUTION
    P = 30,000
    r = 12% = 0.12
    I = 459
    t = ?

    t=I/Pr = 459/30,000(0.12)
           = 459/3600
           = 0.1275 yrs
           = 0.1275 (12)
           = 1.53 months

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Prof. Cris Paner

Discounts (Part II)

Continuing on the last article, the second discount type is known as Cash discount. This is very tricky as a problem solving but it is just as important as the others. Cash discount focuses on the time interval of the payment. And it’s common for you to see terms like 10/15 or n/30. It basically means that a discount of 10% may be deducted from the total amount of payment if it is done in 15 days and if 15 days has passed, the full payment will be given at the end of 30 days starting from the date of invoice.

their is actually no formula to remember in this discount but the crucial part is having a calendar beside you and the terms of the payment. here is a list of days per month:

  January      31

  February    it depends

  March        31

  April          30

  May           31

  June           30

  July            31

  August       31

  September  30

  October      31

  November  30

  December  31

knowing how to compute for discount is also needed.

to remember the dates more easily you can visit this website http://www.eudesign.com/mnems/dayspcm.htm 

paying early is a good practice and it also gives us a special reward of discount!  

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sample problem: An invoice in the amount of P5,500 was dated on September 24 and grants the following terms 10/5, 5/10, and n/30. The date of payment was on October 23.

SOLUTION

since the date of payment was included in the problem, you just need to find if the buyer acquired a discount on the terms given. And starting from September 25, the days that has elapsed is 29 days so no discount will be given. the answer is still P5,500 

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checked by Prof. Cris Paner 

Discounts (Part I)

07/13/2012 - SALE! 30% off! 50% off! and many more % off. These are ways for businesses to attract audience and buy their product. Building a brand loyalty to them is a way for them to grow more money since they are the ones who will buy and use it. And one of the common strategies for them is giving a less.

Discount is the reduction of payment to the product.Different business have different kinds of discounts all for us to be attracted to buy to their product more. But there are also other reasons for discounts like they have new version of the stocks and needs to get rid of it or because it is required by the government like the senior citizen discount. But whatever the reason is, discount is an important factor in businesses. And one should learn how to compute discounts.

their are 3 different ways of computing discount (two will only be tackled and will be broken into two parts) which is:
Trade Discount. And there are 2 sets of formulas to remember:

[Set 1]
Trade Discount = list price x trade discount rate
List Price =     Trade Discount       
                    Trade Discount Rate

Trade Discount Rate = Trade Discount
                                          List Price

[Set 2]
Invoice Price = List Price - Trade Discount
List Price = Invoice Price + Trade Discount
Trade Discount = List Price - Invoice Price

Knowing how to compute for discounts is handy specially when you are short n money and wants to buy this and that.

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sample problem: A study table was placed on a shop with a sign of 30% discount with the original price of P3,500.00. Find the amount of discount and invoice price.

SOLUTION:

   Trade Discount = List Price x Trade Discount Rate
                             = P 3,500 x 0.3
                             = P 1,050

   Invoice Price = List Price – Trade Discount
                         = P 3,500 – P 1,050
                         =  P2,450

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checked by Prof. Cris Paner 

Depreciation Schedule

06/29/2012 - Every material does not last forever and that's why buying something requires a wise decision, especially when used in businesses. By recording the expenses, a company can make sure if the product they bought is helping them rather and not pulling them down. 

They call this as depreciation schedule. It is a record of how much value is left on a piece of equipment or asset as it is being used. But first, one should know how to get the total depreciation and getting the cost. Which is

Total depreciation

   Depreciation = Cost - Scrap Value

Annual Depreciation

   total depreciation
  --------------------
      life value  (P per year,unit, hour)

After getting the necessary requirements, the depreciation schedule can now be done;

Year   /   Hours in operation   /   Depreciation Charge   /       Amount in          /   book value at             
          /      (in machines)        /                                       /   depreciation fund   /     end of year
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 0                      0                                     0                                    0                                  #    << cost      
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 1                      #                                     #                                    #                                 #
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total 

                                                                                        *zero values placed are always zero

Everything has a limit in life and exceeding this limits has it's consequences. So it's better to keep in track about what is happening in not only in our daily lives but also the materials we use. And being a student is not an excuse to this practice! practice! practice!

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 sample problem: A machine costs P55,500, it has a probable life of 100,000 hours and has a scrap value of P5,000. Make a depreciation schedule of the first three years which has the operation hours of 12,000 , 15,000, and 10,000


SOLUTION

the total depreciation  is
        Depreciation = Cost - Scrap Value
                                55,500 - 5,000 = P50,500

          the charge for operating hour is
                                50,500
                              ------------  = 0.51
                               100,000

 Depreciation schedule

Year   /   Hours in operation   /   Depreciation Charge   /       Amount in          /   book value at             
          /      (in machines)        /                                       /   depreciation fund   /     end of year
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 0                      0                                     0                                    0                             55,500           
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 1                  12,000               12,000(0.51)   P6120                      6,120                         49,380                 -------------------------------------------------------------------------------------------------------------------
 2                  15,000               15,000(0.51)      7650                     13,770                        41,730
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3                   10,000               10,000(0.51)      5100                     18,870                        36,630
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total             P37,000                                P18,870               

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checked by Prof. Cris Paner

Bank Reconciliation

06/22/2012 - "Papa, mama i need to pay for my tuition". And your parent will take out a piece of rectangular paper and writes something and gives it to you. We all know what that is, since it is also the most preferred amount of payment but how can one keep track of the money if they just writes, peel it off and gives it away?  

There are two things to remember first is "Bank Reconciliation". It is a process that let's you match the balance between one's accounting record and the bank's statement (provided of course by the bank that is usually given at the end of a month). And second is a "Reconciliation statement". It is the written form where one reports the balance between the two. Then there are also two formulas to remember:

Checkbook Balance           /          Bank Statement
+ errors                              /       +  deposits in transit
----------------------              /       ---------------------------
  total                                /          total
- non-sufficient funds       /        -  outstanding checks
-----------------------           /       ---------------------------

  cash balance     <<<<  same  >>>>   cash balance

As a student, ask your parents to understand it more and as a check holder, it is important to have your reconciliation statement. And lastly, as a last reminder, one must be careful when using checks! Swindlers may be keeping an eye on you.

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sample problem: On June 23,2012, monica recieve her bank statement with a balance of P10,567. While her checkbook balance was P10,110. She found out that the bank has deducted P5.50 because of service charge and that checks 15 has not yet been encashed which amounts to 300. Her deposit of P600 at the end of the month was also late to be included in the bank statement.
 
SOLUTION

Checkbook Balance    P10,872.50        /          Bank Statement         P10,567.00
+ interest                                0.00        /       +  deposits in transit             600.00
-----------------------------------------          /    -------------------------------------------
  total                              10,872.50      /           total                              11,167.00   
- non-sufficient funds              5.50      /      -  outstanding checks           300.00
-----------------------------------------        /    --------------------------------------------
  cash balance       P10,867.00                          cash balance           P10,867.00

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checked by Prof. Cris Paner