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1

Age Problems

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

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

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

4

Set

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.

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|

6

Interest Problems

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

7

Profit and Discount

Cost + Profit = Selling Price
Cost - Loss = Selling Price
Total cost + Gross Profit = Revenue
Marked price - Discount = Selling Price

Example:
Customer paid $24 for a dress. That price represented 25% discount on the original price. What was the original price of the dress?
X - 0.25X=24
X=32

!!! Profit and loss problems are often expressed as a percentage of the cost or the selling price!!
!!!discount expressed as a percentage of the marked price only!!!