Word Problems Flashcards
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
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
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
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}
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|
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
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!!!