word problem on algebra one variable equations

Most of the 7th grade math equations will have this kind of equations with just one variables,before we go deep into this ,let's see what is a variable means.

Varying, in the context of mathematical variables, does not mean change, but rather, dependence on the values of other variable in the expression in which the variable occurs, or dependence of the value of the expression on that of the variable. However, in some languages other than English, one distinguishes between "variables" in functions and "unknown quantities" in equation

Here is a example from algebra 1 word problems

Question:-

The half life of a radioactive substance is 5750 years.If the mass of a sample is 240 after 5000 year.find its initial mass

Answer:-

Let the initial mass be x. It can be solve by algebra calculator online variables,but
now we are finding this value manually as follows

Then current mass 240 is given by

240 = x (1/2)^5000/5750

= x (0.5)^0.87

= x(0.547)

x = 240/0.547 =438.76

The initial mass was 438.76 units.

A problem on QUADRATIC EQUATION

Topic : Quadratic Equation

An equation of the form ax²+bx+c=0 where a, b, c are real numbers and a ≠ 0, is called a quadratic equation.

Question: The standard form of quadratic equation is ax²+bx+c = 0. Where a and b are co-efficient of x and c is a constant. Find the factors of quadratic equation?

Answer:
1^stmethod----> Find the factors of (a * c) such that addition or subtraction of
that factor is the middle term b.
2^ndmethod----> using quadratic formula

-b + √ b2 - 4ac
_______________
      2a

Example of 1^stmethod
x² + 5x + 6 = 0
Here a = 1, b = 5, c = 6
x² + 5x + 6 = 0
x2 +2x + 3x + 6 = 0
x(x + 2) +3 (x + 2) = 0
(x + 2) (x + 3) = 0
x + 2 = 0 or x + 3 = 0
x = - 2 or x = - 3
or x = -2 , -3

A problem on geometric sequence

If a sequence of values follows a pattern of multiplying a fixed amount (not zero) times each term to arrive at the following term, it is referred to as a geometric sequence. The number multiplied each time is constant .

The fixed amount multiplied is called the common ratio, r, referring to the fact that the ratio (fraction) of the second term to the first term yields this common multiple. To find the common ratio, divide the second term by the first term.

Let's a example on this.

Question:-

What is the next term in the geometric sequence 16,-4,1,-1/4

Answer:-

given terms 16,-4,1,-1/4

first term = a =16

common ratio=r= t2/t1

r = -4/16 = -1/4

5 th term =r5=a*r^5-1

= 16*(-1/4)⁴

=16*(1/256)

= 1 / 16 is the answer

For more help on this ,you can reply me.

Find the equation of a line

Topic:- equation of a line

The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.
If you know two points that a line passes through, this page will show you how to find the equation of the line.

The equation of a line point slope form

(y-y1) = m (x-x1)
This math help gives you a example roblem ...

Question:-

Find the equation of a line point slope form for (4,10)and the slope of the line is 3.

Answer:-

 let us assume

  ( 4 , 10 )
   x1   y1

 and  slope m=3


The equation of a line point slope form

 (y-y1) = m (x-x1)

Substitute the values

( y -10 ) =  3 ( x -4 )
 

   y-10 = 3x-12
    +10     +10
----------------------
     y  = 3x-2

So y=3x-2 is the Answer.

For more help on this ,Please reply me.

problem on Substitutoring method

Topic :Substitution Method

If we have 2 equations ,We can solve them by substituting one on another,This is called Substitution method.We can solve the equations with out any complexity like elimination method.

here is one similar kind of example ,shows how to solve equations


Question:-

           1
Solve y = ---- x + 3 and   y=2x-1
         2

by using sustitution method.

Solution:-

Given


    1
y = ---- x + 3 -------Equation-1
    2

and   y=2x-1 -------Equation-2


Here equation 2 can be substituted in equation 1

         1
 2x-1 = ---- x+3
         2
   +1        +1  Add 1 bothsides
-------------------
         1
 2x   = ----x+4
         2

  1       1             1
- ---x  - ---x subtract ---x
  2       2             2
------------------
   1
2x- ---x = 4
   2
3
----- x = 4
2

3
----- x * 2 = 4 * 2 (multiply by 2
2

3x = 8
  
      8
 x = ----  is the Answer
      3

For more help ,Please reply me .

Question to Find the Slope of given Straight line Equation

Here is a Linear Programming problem on Slope and y intercept of a Straight line, Straight line equation is a linear equation in two variables.
Slope is a the ratio of the altitude change to the horizontal distance between any two points on the line.
y-intercept is the y-value of the point where the graph of the function or a relation intercepts the y-axis of the rectangular coordinate system (x = 0)

Topic : Slope and y-intercept of a Straight Line

This the simple and direct question to find slope and y intercept.

Problem : Given straight line is x + y - 7 = 0, find the slope and y-intercept of the straight line.
Solution :
Slope is always denoted by 'm'
and Slope = - Co-efficient of x / Co-efficient of y
So from the given straight line x + y - 7 = 0
=> - 1/1 = - 1
Slope = - 1

Now to find y-intercept
put x = 0 in the given straight line linear equation,
So x + y -7 = 0
y - 7 = 0
=> y = 7
=> y-intercept is (0,7)

You can find lot more problems related to the linear programming problems in geometry help and algebra help.

Problem on Elliptical figure and find Maximum height.

An Elliptical figure with maximum height can be shown as given in the below word problem.

Topic : Geometry Construction of Ellipse.

For any word problem a geometrical construction is required to predict what the word problem mean.

Question : An arched footbridge over a 100 ft river is shaped like half an ellipse. The maximum height of the bridge over the river is 20 feet.

Find the height of the bridge over a point in the river exactly 25 ft from the center of the river.

Solution :















Geometrical construction for the word problem can be drawn as shown in the above figure,

Now let P be the point 25ft from center
So from the point P till the top of the bridge, we have (20 + 25) ft

= 45 ft

Height of bridge from P = 45 ft.


For more help leave your queries in comment box and Geometry help or calculus help will get back to you for your assistance.

Question on Calculating Number of Marbles

Topic : Word Problem on Number of marbles

Question : Find the marbles with Al, when Dani has got 4 marbles with him and Al gives half of his marbles to Bev , and Bev gives half to Carl, Carl gives half to Dani.

Solution :
Let the number of marbles with Al be "x"
So he gives half to Bev
So number of marbles with Bev is "x/2"
and again Bev gives half to Carl

So number of marbles with carl is x/2 divided by 2 = "x/4"
then carl gives again half of his marbles to Dani
As number of marbles with Dani is x/4 divided by 2 = "x/8"
we know that the number of marbles dani has = 4

So x/8 = 4
x/8 * 8 = 4 * 8
x = 32

A Simple Problem Simplification

Topic : Simplification

Problem : (1/a - 1/b) ÷ (1/a² - 1/b²)

Solution :

A Simple Solved Problem on Factorization and Simplification

Topic : Simplification

Question : Simplify 3/(m-4) - (m+2) / (m - 3m - 4) = 1/(2m+2)

Solution :

Problem on Linear Equations to Find the Unknown Value of a Variable

Topic : Linear Equations

Problem : Solve 2x + 3y = 4 and 3x - 2y = 1

Solution :
2x + 3y = 4 --------------(1)
3x - 2y = 1 --------------(2)

Multiply equation (1) by 3 and equation (2) by 2 then,
6x + 9y = 12 ----------- (3)
6x - 4y = 2 ------------ (4)
Subtraction (4) by (3) then,
+13y = 10
y = 10/13

Substitute the value of y in equation (1)
2x + 3y = 4
2x + 3(10/13) = 4
2x + 30/13 = 4
2x = 4 - 30/13
2x = (52-30)/13
2x = 22/13
x = 11/13

A Simple Problem on Integration

Topic : Integration

Problem : Integrate 1/x² * (x+2)³

Solution :

Deriving the value of Cos 11π/4

Topic : Trignometric Value of Cos 11 π/4

Problem : Find the value of cos(11π/4)

Solution :
General Formula is Cos θ = Cos (2π - θ)
So Cos 11 π/4 = Cos (2 π - 11 π/4)
= Cos (-3 π/4)

Again by another formula
Cos θ = -Cos (π + θ)
So -Cos (-3 π/4) = -Cos (π + (-3 π/4))
= -Cos (π/4)

Now Cos (π/4) = 1/√2
So -Cos (π/4) = - 1/√2

Word Problem on Simple Interest

Topic : Investment and Simple Interest

Question : Roberto invested some money at 7%, and then invested $2000 more than twice this amount at 11%. His total annual income from the two investments was $3990. How much was invested at 11%?

Solution :
Let the amount invested at 7% be x
then the amount invested at 11% will be $(2x+2000)
Now the total annual income from these investments = $ 3990
So, the equation will be ,
7/100 *x +11/100 * (2x + 2000) = 3990
0.07x + 0.11(2x + 2000) = 3990
0.07x + 0.22x + 220 = 3990
0.29x +220 = 3990
subtract both sides by 220
0.29x = 3770
divide both sides by 0.29
x = 3770/0.29
x =13000

So, amount invested at 7% = $ 13000
Therefore the amount invested at 11% = 2x + 2000
= 2(13000) + 2000
=26000 + 2000
= $ 28000

Question on Factorization of trinomial

Topic : Factorization

Questions : Factorization of trinomial
Factorise x^2+7x+12

Solution :
X^2 +7x +12 has two binomial factors with the product of the first term as x^2
Thus we can write X^2+7x+12 + (x +a) (x +b)
a and b are the missing terms
The product of the missing terms is 12 and their sum is 7 Let us examine the
Factors of 12
1x 12 = 12 but 1 + 12=13 ≠ 7
2x 6 =12 but 2 +6 = 8 ≠ 7
3 x 4 =12 here 3 + 4=7 as required
Thus we factorise X^2 + 7x +12 = (x+3 ) (x+4)

A Word Problem on Milkman and Domesticated Animals with Him

Topic : Word problem on Milkman and domesticated animals.
Question : A milkman has some buffaloes cows and goats. He has goats equal to 5/2 times the number of cows and cows equal to 3/2 times the number of buffaloes. If there are 150 animals with the milkman, how many of each category has he with him?

Solution : Let the Number of buffaloes = Y

Number of cows = Y x 3/2 = 3Y/2 (3/2 times of buffaloes)

Number of Goats = 3Y /2 x 5/2 = 15Y /4 (5/2 times of cows)

Total number of animals = Y + 3Y/2 + 15Y/4 (Adding all of them)

= (4Y + 6Y + 15Y)/ 4

= 25Y / 4

According to the information given total animals = 150

Therefore 25Y / 4 = 150

Y = 150 x 4/ 25 = 24

Number of buffaloes = 24 (As we assumed number of buffaloes as Y)

Number of Cows = 3(24)/2 = 36 (As Cows = 3Y/2)

Number of Goats = 15(24)/ 4 = 90 (As Goats=15Y/4)

Question on How to Find Square of Specific Numbers

Topic : Square of numbers

Question : How to Find Square of numbers ending with 5?

Solution :
Let us take an example of a number say A5
a two digit number ending with 5 Square of A5 = A(A + 1)/25
means that the square always have last two digits as 25 and the other leftmost
digits will be the product of digit other than 5 and its next consecutive digit.
For example : 65 x 65 = 6 x 7 / 25 = 42 / 25 = 4225 (/ is written for partition between two operations)
Square of 125 = 12x13/25 = 15625
and you can find as many squares of the numbers ending with 5.


If you have any Queries, feel free to ask us.

Question on Equation of Parabola

Topic : Equation of parabola.

Question : y=(x-4)(x+2), find the x-intetcept and the vertex.

Answer :
This is equation of a parabola.
If you put in y=0
x-intercepts are (4,0) and (-2,0) or 4 & -2
equation can be written as
y= x^2-2x-8
for parabola of form y= ax^2+bx+c the vertex is given by ( -b/2a, (-b^2+4ac)/2a)
here a =1 , b=-2 , c= -8
so vertex is ( 2/2, (-4-32)/2)
= (1,-18) is the vertex

If you need more explanation, please leave the comments about the topic discussed above.