Translating words into Algebraic Expression

Definition: Translating words into algebraic expression is the process of translating the word problems into an algebraic expression which can be used to solve the word problem and produce the solution for the given words problem.

Problems of translating words into algebraic expression:

Problem 1:

Flowers shop has thirty Roses and forty Lilly. How many pieces of flowers does flowers shop have?

Solution:

Let a = Total number of Flowers in the flowers shop.
The sum of thirty Roses and forty Lilly is equal to the total number of flowers in the flowers shop. It translates the words problem into an algebraic expression.
a = 30 + 40

Solve this expression.

Let a = Total number Pieces of Flowers in the flowers shop
a = 70.

There are 70 Pieces of Flowers in the flowers shop.

Problem 2:

The sum of twice a number plus 20 is 86.Find the number.

Solution:

In words problem, the word is means equals and the word and means plus.
Translating words problem into an algebraic expression
the sum of twice a number and 20 equals 86.
Write an expression

2X + 20 = 86

Solve this expression using the variable.

2X + 20 = 86 (Expression)

2X + 20 – 20 = 86 - 20 (subtract by -20 on both sides)

2X= 66

X = 33 (Divided by 2 on both sides we get the result)

Solution to the problem is 23.

Hope you like the above example of Translating words into Algebraic Expression
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Ratio and Proportion

Ratio: Ratio is the numerical relationship between two quantities of the same kind. The first quantity is called the antecedent and the second quantity is called the consequent.

Proportion: a, b, c and d are said to be proportion if a : b = c : d.
a and d are called the extremes, b and c are called the means. a, b, c and d are called first proportion, second proportion, third proportion and fourth proportion respectively.

Types Of Ratios and Proportion:

Ratios are classified in to six types:

1) Duplicate ratio:The ratio of the squares of the two numbers.Ex: 9:16 is the duplicate ratio of 3:4.

2) Triplicate ratio:The ratio of the cubes of the two numbers.Ex: 27:64 is the triplicate ratio of 3:4.

3) Sub-duplicate ratio:The ratio between square root of the two numbers.Ex: 4:5 is the sub-duplicate ratio of 16:25.

4) Sub-triplicate ratio:The ratio between the cube roots of the two numbers.Ex: 4:5 is the sub-triplicate of 64:125.

5) Inverse ratio:If the two terms in the ratio interchange their places,then the new ratio is inverse ratio of the first.Ex: 9:5 is the inverse ratio of 5:9.

6) Compound ratio:The ratio of the product of the first term to that of the second term of two or more ratios.Ex: 3/4,5/7,4/5 and 3/5 is 3/4 x 5/7 x 4/5 x 3/5 = 9/35.

Proportions are classified in to four types:

1) Continued proportion:In the proportion 8/12=12/18, 8,12,18 are in the continued proportion.

2) Fourth proportion:If a:b=c:x,then x is called forth proportion of a,b and c.The fourth proportion of a,b.c =bc/a

3) Third proportion:If a:b=b:x,then x is called third proportion of a and b.Third proportion of a,b =b^2/a

4) Second or mean proportion: If a:x=x:b,then x is called second or mean proportion of a and b.Therefore mean proportion of a and b =Root of(ab)

Simple Interest and Compound Interest

Interest: Interest is the amount of money we pay for the use of some amount of money

There are two types of interests,

a) simple interest: Simple interest is the Interest paid / compensated only on the original principal, not on the interest accrued

b) compound interest: interest means that the interest Which includes the interest calculated on principal amount

Algebra Formula to find simple interest :

Simple interest I = PRT

Where, P is the Principal amount, R is the Rate of interest, N is Time duration.

When we knows interest I we can find p, n or r using the same formula ,

Different forms of algebra simple interest formula

Algebra formula to find Compound Interest:

FV = PV (1+r)ⁿ

PV is the present value

r is the annual rate of interest (percentage)

n is the number of years the amount is deposit or borrowed for.

FV = Future Value is the amount of money accumulate after n years, including interest.