problem on solving linear equations

Topic:-linear equation

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.

Linear equations can have one or more variables. Linear equations occur with great regularity in applied mathematics. While they arise quite naturally when modeling many phenomena, they are particularly useful since many non-linear equations may be reduced to linear equations by assuming that quantities of interest vary to only a small extent from some "background" state.

Question:-

solve |5b-3| = |3b+7|

Answer:-
This math help is from linear equations.

This is of the form |a|=|b|

which implies a = +b
        or a = -b

Using this we get

    5b-3=+(3b+7)

    5b-3=-(3b+7)

5b-3 =+(3b+7)|  5b-3 =-(3b+7)
            |
5b-3 = 3b+7 | 5b-3 = -3b-7
            |
bring 3b    |
left        | bring 3b left
hand side   | hand side
            |
5b-3b=7+3   | 5b+3b= -7+3
            |
2b = 10     | 8b= -4
            |
b = 5       | b = -4/8
            |
            | b = -1/2

So b= 5 or -1/2 is the answer

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How to solve time and work problems

Topic :- Time and Work

Time and work problems are very important for test preparation when you are out of school for long period .
The time will be given and the amount of work done in that time period needs to be calculated and vice versa .

Here is a simple Time word problem Given ,Which will give an idea of solving workwordproblems
as well.
Question :-

Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?

Answer:-

Jim can fill the pool in 30 min.
So in 1 min,jim can fill 1/30 th part of pool.

Similarly in 1 min,Sue can fill 1/45th part of pool.

Now 1 1/2 hours = 60+30=90 min.

So in 1 min,Tony can fill 1/90 th part of pool.

Now,if all of them work together,then in 1 min,the part of the tak filled is

   1     1      1
= --- + ---- + ----
  30     45     90

Lcm=90

So by equalizing the deniminators

 1*3      1*2     1*1
------ + ----- + -------
 30*3     45*2    90*1

    3        2        1
= ------ + ------ + ------
    90       90      90

      3+2+1
=    ----------
      90

   6
= ------
   90
   1
= ----
   15

Hence,If they all work together ,The tank will be filled in 15 minutes.


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Problem on parallelogram, Finding Area of parallelogram

Geometry construction section in math consists of geometrical figures like parallelogram rectangle, trapezium where we find few terms like linear pair, supplementry angles.
If a pair of angles are adjacent as well as supplementary then they are said to form a linear pair

Topic : Area of parallelogram

Below example also prove how the necessary statements are considered.

Question : In the following figure, NDBA is a rectangle, AN = NG, BF = DB, GD = 11, and DF = 8√2. What is the area of parallelogram GDFA?

State all the statements that are necessary in your proof along with their reasons in a two-column table.

Solution :

If you have any queries please do write to our geometry help.

Question on Integrating a Given Function

Here is a Multi choice question to Evaluate function by Integration.
You can find similar set of questions at TutorVista Blogs.

Topic : Integrating a Function.

Below example will help you to identify correct choice and get reasons for, why remaining choices are incorrect.

Question : At what point in the interval [0, √3] does the function y=x² - 1 assumes its average value.
a. -1
b. 1
c. 1.5
d. 1.7

Solution :
Choice b is correct.
Average value = 1/(√3 - 0)₀∫^√3 (x² - 1)dx = 0
And x² – 1 = 0
Therefore, y= x² -1 assumes its average at x = 1

Choice a is incorrect as -1 is not in the interval [0, √3]

Choice c is incorrect as 1.5 does not satisfy the equation x² -1=0

Choice d is incorrect as 1.7 does not satisfy the equation x² -1=0


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Question on Solving a Word Problem using Proportion Method

Topic : Proportion Method

Question : Nicole enlarged the size of rectangle to a height of 28 in. What is the new width if it was originally 6 inch wide and 7 inch tall?
a). 24in. b). 112 in. c) 2in. d) 7in.

Solution :
Forming the proportion :
6 : 7 = X :28
Using law of proportion, that product of extremes is equal to the product of means
6 x 28 = 7 x X
X = 28 x 6 /7
X = 168 / 7
X = 24
So, the width is 24 inch.

Question on Percentage of Sugar Solution

Topic : Word Problem on Percentage

Question : How many gallons of 15% sugar solution must be mixed with 5 gallons of 40% sugar solution to make 30% sugar solution?

Solution :

%sugar ---gallons
15% -------- x
40% -------- 5
30 % ------- x+5
so, 15% of x+ 40% of 5 = (x+5) 30%
0.15x+ 2 = 0.3x+15
x= 0.5/0.15
x= 10/3
10/3 gallons of 15% sugar solution is mixed with 5 gallons of 40% sugar solution to
make 30% sugar solution.

A Simple Simplification

Topic : Simplification

Problem : Solve ax - 2 a y - 3 b x + 4 b y = 0

Solution :