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## Math Problems Solver

## Solved Examples

**Question 1:**Find the value of 'a' at x = 2 .

$\sqrt{2x + 3a}$ = 5

**Solution:**

Step 1:

Given equation

$\sqrt{2x + 3a}$ = 5

Step 2:

Squaring both side to remove the radical

=> 2x + 3a = 25

=> 3a = 25 - 2x ......................(1)

Step 3:

Substituting x = 2 in equation (1),

=> 3a = 25 - 2 * 2

=> 3a = 25 - 4 = 21

=>

Given equation

$\sqrt{2x + 3a}$ = 5

Step 2:

Squaring both side to remove the radical

=> 2x + 3a = 25

=> 3a = 25 - 2x ......................(1)

Step 3:

Substituting x = 2 in equation (1),

=> 3a = 25 - 2 * 2

=> 3a = 25 - 4 = 21

=>

**a = 7****Question 2:**Solve quadratic equation 6x

^{2}+ 25x - 25 = 0

**Solution:**

Given quadratic equation 6x

=> 6x

Factors the left hand side of the equation,

=> 6x

=> 6x(x + 5) - 5(x + 5) = 0

=> (6x - 5)(x + 5) = 0

=> either 6x - 5 = 0 or x + 5 = 0

=> 6x = 5

=> x = $\frac{5}{6}$

or x = - 5

=> Solutions of equation are

^{2}+ 25x - 25 = 0=> 6x

^{2}+ 25x - 25 = 0Factors the left hand side of the equation,

=> 6x

^{2}+ 30x - 5x - 25 = 0=> 6x(x + 5) - 5(x + 5) = 0

=> (6x - 5)(x + 5) = 0

=> either 6x - 5 = 0 or x + 5 = 0

=> 6x = 5

=> x = $\frac{5}{6}$

or x = - 5

=> Solutions of equation are

**x = 0.83, - 5.****Question 3:**Solve the system of equations

- 3 + 5x = y

2x + 5y = 12

**Solution:**

Given

- 3 + 5x = y

2x + 5y = 12

or

5x - y = 3 ................(1)

2x + 5y = 12 ...............(2)

No equation given solved for a variable, Equation (1) can be solved literal for y,

y = 5x - 3

Substituting the expression in equation (2)

=> 2x + 5(5x - 3) = 12

=> 2x + 25x - 15 = 12

=> 27x - 15 = 12

=> 27x = 12 + 15 = 27

=> x = 1

Substituting x = 1 in y = 5x - 3,

y = 5 x 1 - 3 = 5 - 3 = 2

=> y = 2

Hence the solution to the given system,

- 3 + 5x = y

2x + 5y = 12

or

5x - y = 3 ................(1)

2x + 5y = 12 ...............(2)

Step 1:Step 1:

No equation given solved for a variable, Equation (1) can be solved literal for y,

y = 5x - 3

Substituting the expression in equation (2)

=> 2x + 5(5x - 3) = 12

=> 2x + 25x - 15 = 12

=> 27x - 15 = 12

=> 27x = 12 + 15 = 27

=> x = 1

Step 2:Step 2:

Substituting x = 1 in y = 5x - 3,

y = 5 x 1 - 3 = 5 - 3 = 2

=> y = 2

Hence the solution to the given system,

**x = 1 and y = 2.**## Math Solver Word Problems

## Solved Examples

**Question 1:**The length of a rectangle is 20 more than twice is width. If the perimeter is 280 feet, how wide is the rectangle.

**Solution:**

Let width of the rectangle = x

then length = 2x + 20

(Length be 20 more than twice its width)

Perimeter = 280

We know, Perimeter of rectangle = 2(length + width)

=> 2(length + width) = 280

=> 2(2x + 20 + x) = 280

=> 2(3x + 20) = 280

=> 6x + 40 = 280

=> 6x = 240

=> x = 40 feet

=> Width of the rectangle = 40 feet.

then length = 2x + 20

(Length be 20 more than twice its width)

Perimeter = 280

We know, Perimeter of rectangle = 2(length + width)

=> 2(length + width) = 280

=> 2(2x + 20 + x) = 280

=> 2(3x + 20) = 280

=> 6x + 40 = 280

=> 6x = 240

=> x = 40 feet

=> Width of the rectangle = 40 feet.

**Question 2:**Macshon is now twice as old as Stefy, but five years ago, he was three times as old as she was. How old is Macshon now.

**Solution:**

Let the present age of Stefy = x

Macshon is twice as old as Stefy

=> Age of Macshon = 2x

Age of Stefy = x - 5

and age of Macshon = 2x - 5

The problem states:

Macshon three times as old as Stefy was

=> 2x - 5 = 3(x - 5 )

=> 2x - 5 = 3x - 15

=> x = 10, age of Stefy

So age of Macshon = 2 * 10 = 20

Macshon is twice as old as Stefy

=> Age of Macshon = 2x

**Five years ago:**Age of Stefy = x - 5

and age of Macshon = 2x - 5

The problem states:

Macshon three times as old as Stefy was

=> 2x - 5 = 3(x - 5 )

=> 2x - 5 = 3x - 15

=> x = 10, age of Stefy

So age of Macshon = 2 * 10 = 20

Hence Macshon is of 20.Hence Macshon is of 20.