**CHAPTER 7**

**ADVANCED CONCEPTS**

**In many problems, it is necessary to use complex word combinations to express an idea or dimension.**

We have already discussed the concept of ‘ft. x ft.’ to express the area of a room as ‘square feet’.

Sometimes, two

We have already discussed the concept of ‘ft. x ft.’ to express the area of a room as ‘square feet’.

Sometimes, two

*different*words need to be multiplied together to show the idea. One common example of this is:**KILOWATT HOUR**

**What exactly does this mean ? The word ‘Kilowatt’ means ‘1,000 watts’ (‘Kilo’ is a metric system term**

**for ‘1,000’). Fine !**

**Where does the word ‘hour’ come in ?**

A ‘watt’ is an electrical term for ‘power’. When you buy a ‘100 watt’ lamp, the ‘100’ indicates how much

A ‘watt’ is an electrical term for ‘power’. When you buy a ‘100 watt’ lamp, the ‘100’ indicates how much

**power is required to operate it. But power is not the only consideration ! ......**

**If your neighbor operates HIS lamp bulb all night while you only operate your for 3 hours, the**

**electric company will charge him more. Why ?**

**Because the electric company's rates are based upon "ENERGY" not "POWER" ! Thus, we need a**

**'word phrase' for "ENERGY". Do you remember Rule 12 ? (Re-read it)**

**KILOWATT HOUR = KILOWATT x HOUR**

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**Another concept that is confusing to many (including college graduates) is the concept of**

**‘interest on a loan’.**

**RULE # 52 INTEREST IS THE AMOUNT MONEY A LENDER CHARGES A BORROWER FOR**

**USING THE LENDER’S MONEY. INTEREST CHARGED IS DEPENDENT UPON :**

__AMOUNT, LENGTH OF TIME IT WAS HELD AND RATE OF__

__INTEREST.__**Most adults understand Rule #52 in a general sense. However, the key phrase which causes confusion**

is ‘length of time it was held’. The word ‘it’ obviously refers to the amount of money borrowed.

(This is called: ‘principal’ ). If you borrowed $ 100 for a year, this means that you (the borrower)

is ‘length of time it was held’. The word ‘it’ obviously refers to the amount of money borrowed.

(This is called: ‘principal’ ). If you borrowed $ 100 for a year, this means that you (the borrower)

**should****keep the entire $100 principal for a full year !****If you repay**

*any*part of the principal during the year, then that would not be true !--------------------------------------------------------------------------------------------------------

**Another important concept can be called ‘parallel jobs’. ‘Parallel’ means ‘side-by-side’; ‘parallel jobs’**

**refers to two or more things doing the same job at the same time, each contributing a portion towards**

**completing the overall job.**

For example, filling a swimming pool with two water hoses. If each hose were the same size, we would

For example, filling a swimming pool with two water hoses. If each hose were the same size, we would

**correctly guess that both hoses could fill the pool in half the time it would take a single hose to fill it by itself.**

What if the hoses were not the same size (diameter) ?

What if the hoses were not the same size (diameter) ?

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**Click for answers PROBLEMS**

**1. The electric company charges $0.03 per kilowatt hour. What will it cost to operate 15 lamps**

**(60 watts each) for 10 hours and 5 hair dryers (200 watts each) for 2 hours ?**

**2. A man borrowed $2000 from a bank. Four(4) months later, he repaid the bank $2100**

**(including interest charge). W**

**hat is the true annual interest rate he was charged?**

**3. The earth has a circumference of 25,000 miles. If the circumference increased to 25,001 miles,**

**by how many yards would the radius increase ?**

**4. Two brick layers can build a house in 30 days. If the first can build it himself in 45 days,**

how long would it take the second to build it alone ?

how long would it take the second to build it alone ?

__BONUS QUESTION__: THIS IS NOT A BRAIN TEASER OR PUZZLER. IT CAN BE SOLVED BY**DEVELOPING A**

**RELATIVELY SIMPLE EQUATION !**

**Joe is 24 years old. Joe is twice as old as Bill was when Joe was as old as Bill is.**

How old is Bill ?

How old is Bill ?