Algebra solving solution
Introduction:
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures.In mathematics, a quadratic equation is a polynomial equation of the second degree. The way of generalizing arithmetic is called algebra. The part of algebra called elementary algebra is often part of the curriculum in secondary education and introduces the concept of variables representing numbers.
Source Wikipedia.
Algebra solving solution problems:
Algebra solving solution problem 1:
Solve Linear Equations 3x + 2y = 4,
x + 4y = 2
Solution:
3x + 2y = 4 equation 1,
x + 4y = 2 equation 2
Multiply by 3 in equation 2
3 ( x + 4y = 2) => 3x + 12y = 6 equation 3
Subtract equation 1 and equation 3
3x + 2y = 4 equation 1,
(-)(3x + 12y) = (-) 6 equation 2
0 - 10y = - 2
After subtracting, - 10y = - 2
y = ` (2/10)`
= ` (1)/5`
Substitute the y value in equation 1
3x + 2`((1)/5)` = 4
15x + 2 = 4 * 5
15x + 2 = 20
15x = 20 - 2
15x = 18
Divided by 15 on both side `(15x)/15 ` =` 18/15`
x = `18 / 15 `
Answer: x = `18 / 15 ` and y =` (1)/5`
Algebra solving solution problem 2:
Simplify the expression (3 + x) + x (1 - 4x) + `10/2`
Solution:
Step 1: clear the parentheses,
3 + x + (1 × x) - (4 x × x) + `10 / 2`
Step 2 :combining like terms,
3 + x + x - 4x2 + 5
Step 3: Add constants,
3 + 2x - 4x2+ 5
8 + 2x - 4x2
So, Answer for Free algebra home work problem - 4x2 + 2x + 8
Algebra solving solution problem 3:
Pipe X can fill the tank in 5 hours and pipe Y can fill the tank in 7 hours respectively. When the tank is full, it can be drained by pipe Z in 4 hours. If x, y, z pipes are opens at the same time, how long will it take to fill up the tank?
Solution:
Step 1: Assign variables
Let a = time taken to fill up the tank
Step 2: Use the formula
The drain water z is subtracted
` 1 / 5` + ` 1 / 7` - `1 / 4` = `1 / a`
Step 3: Solve the equation
The LCM of 5, 7 and 4 is 140.
Multiply both sides with 140
`140 / 5 ` + ` 140 / 7` - `140 / 4` = `140 / a`
28 + 20 - 35 = `140 / a`
13 = `140 / a`
13a = 140
a = `140/ 13`
a = `10` `10/13`
Answer: ` 10 10/13` hours.
Algebra solving solution problem 4:
In a meeting hall, there are 608 persons consists of men, women, and children. There are five times as many men as children, and twice as many women as children. How many of women are there?
Solution
Let 'x' be the number of children. Then
5x be the number of men and
2x be the number of women.
So, the equation is
x + 5x + 2x = 608
8x = 608
x =`608/8`
x = 76
Answer: Number of women = 2x = 2(76) = 152
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures.In mathematics, a quadratic equation is a polynomial equation of the second degree. The way of generalizing arithmetic is called algebra. The part of algebra called elementary algebra is often part of the curriculum in secondary education and introduces the concept of variables representing numbers.
Source Wikipedia.
Algebra solving solution problems:
Algebra solving solution problem 1:
Solve Linear Equations 3x + 2y = 4,
x + 4y = 2
Solution:
3x + 2y = 4 equation 1,
x + 4y = 2 equation 2
Multiply by 3 in equation 2
3 ( x + 4y = 2) => 3x + 12y = 6 equation 3
Subtract equation 1 and equation 3
3x + 2y = 4 equation 1,
(-)(3x + 12y) = (-) 6 equation 2
0 - 10y = - 2
After subtracting, - 10y = - 2
y = ` (2/10)`
= ` (1)/5`
Substitute the y value in equation 1
3x + 2`((1)/5)` = 4
15x + 2 = 4 * 5
15x + 2 = 20
15x = 20 - 2
15x = 18
Divided by 15 on both side `(15x)/15 ` =` 18/15`
x = `18 / 15 `
Answer: x = `18 / 15 ` and y =` (1)/5`
Algebra solving solution problem 2:
Simplify the expression (3 + x) + x (1 - 4x) + `10/2`
Solution:
Step 1: clear the parentheses,
3 + x + (1 × x) - (4 x × x) + `10 / 2`
Step 2 :combining like terms,
3 + x + x - 4x2 + 5
Step 3: Add constants,
3 + 2x - 4x2+ 5
8 + 2x - 4x2
So, Answer for Free algebra home work problem - 4x2 + 2x + 8
Algebra solving solution problem 3:
Pipe X can fill the tank in 5 hours and pipe Y can fill the tank in 7 hours respectively. When the tank is full, it can be drained by pipe Z in 4 hours. If x, y, z pipes are opens at the same time, how long will it take to fill up the tank?
Solution:
Step 1: Assign variables
Let a = time taken to fill up the tank
Step 2: Use the formula
The drain water z is subtracted
` 1 / 5` + ` 1 / 7` - `1 / 4` = `1 / a`
Step 3: Solve the equation
The LCM of 5, 7 and 4 is 140.
Multiply both sides with 140
`140 / 5 ` + ` 140 / 7` - `140 / 4` = `140 / a`
28 + 20 - 35 = `140 / a`
13 = `140 / a`
13a = 140
a = `140/ 13`
a = `10` `10/13`
Answer: ` 10 10/13` hours.
Algebra solving solution problem 4:
In a meeting hall, there are 608 persons consists of men, women, and children. There are five times as many men as children, and twice as many women as children. How many of women are there?
Solution
Let 'x' be the number of children. Then
5x be the number of men and
2x be the number of women.
So, the equation is
x + 5x + 2x = 608
8x = 608
x =`608/8`
x = 76
Answer: Number of women = 2x = 2(76) = 152