Flashcards in Word Problems Deck (7)

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1

## Age Problems

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We start by letting x be person's current age and then the person's age y years ago will be x-y and the person's age y years in future will be x+y

Делается таблица

Person A | Person B

Age Now | X | X+Z

y years ago | X-Y| X+Z-Y

y years from now| X+Y| X+Z+Y

2

## Work Problems

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Rate=Work/Time

R=W/T

Examples of Rate: 10 items per hour, 5 litres per second,

Time - 6 hours

Work: 3 items, 10 liters, 1 tank

Working together:

R comined= R1+/- R2

Pipes:

two inlet pipes. R comined = R1 + R2

one inlet, one outlet : R comined = R1-R2

Sometimes the total amount of work is not known.

W=1. R=1/t

1/tcombined=1/t1 + 1/t2

3

## Mixture problems

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Soluton 1: m1 (weight), k1% (concentration)

Solution 2: m2(weight), k2%(concentration)

Mres=m1+m2

k1% < Kres% < k2%

if k1=k2 -> Kres=k1=k2

m1Xk1 + m2 X k2 = (m1+m2) x Kres

Лучше порой использовать метод-крестика.

Соотношение абсолютный значений концентраций даст возможность высчитать массы растворов

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## Set

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Set - collection of numbers or other objects

elements - objects of the set

|S| - finite number of elements

S = {-5,0,1} , |S|=3

The order in which elements are listed in a set does not matter

If all elements of the set S are also elements of a set M, then S is a subset of M.

S= {-5,0,1}, M ={-5,0,1,4,10}

5

## Sets. Hard. Union.

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union of S and T is the set of all elements that are in set S or Set T or in both. Union - U.

The intersection of S and T - set of all elements that are both in S and in T. intersection S П T

Example:

S= {-5,0,1}, M ={-5,0,5,17}

S U T = {-5,0,5,17,1}, S П T = {-5,0}

|S U T|=|S| + |T| - |S П T|

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## Interest Problems

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Simple annual interest rate

Interest = (Principle) x (Interest Rate) x (time) -сколько он заработает с процентов

interest rate = decimal

time = years

Final Balance = Principle + Interest rate = Principle (1+IR X time)

Total Interest from both accounts = Interest from first account + interest from second account

Interest is compounded, when interest is computed on the principle as well as on any interest already earned.

Final balance = (Principle) x (1 + IR/C)^(Time X C)

C- is equal number of times compounded annually

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