Online help for algebra makes you thankful for the internet all over again, doesn't it? A multitude of free online algebra problem solvers give you your answers instantly. But the real test is, do you know what they did and how they did it? Just looking at how a problem is solved is not going to be any help at all. If you've tried to cram before an algebra test by just glancing through your text, you already know this by now. That's not to say that online algebra problem solvers can't help. Tutoring sites offer comprehensive solutions to your algebra woes by providing a step by step algebra problem solver. The idea is for you to learn what you want to, when you want to.

Solved Example

Area and perimeter of a rectangular rug is 84 square feet and 38 feet. Find the dimensions of the rectangular rug.

Let 'x' be length and 'y' be width of the rectangular rug.

Given,

Area of rectangular rug = 84 $feet^2$

and perimeter = 38 feet

[ Area of rectangle = length * width]

[Perimeter of rectangle = 2(length + width)]

=> xy = 84

=> y = $\frac{84}{x}$ .........................(1)

and

2(x + y) = 38 ........................(2)

Put (1) in (2)

=> 2(x + $\frac{84}{x}$) = 38

=> x + $\frac{84}{x}$ = $\frac{38}{2}$

=> x + $\frac{84}{x}$ = 19

=> $x^2$ + 84 = 19x

=> $x^2$ - 19x + 84 = 0

which is quadratic equation

Solve for x, $x^2$ - 19x + 84 = 0

=> $x^2$ - 19x + 84 = 0

=> $x^2$ - 7x - 12x + 84 = 0

=> x(x - 7) - 12(x - 7) = 0

=> (x - 12)(x - 7) = 0

either x - 12 = 0 or x - 7 = 0

x - 12 = 0

=> x = 12

So **Length of rectangular rug = 12 feet**

x - 7 = 0

=> x = 7

So **Length of rectangular rug = 7 feet**

Solved Example

Let the present age of the son = x years

Therefore father's age = 5x

(Father is 5 times his son's age)

**Step 1:**

After 15 years:

Son's age = x + 15

and father's age = 5x + 15

**Step 2:**

Father's age = Thrice the son's age

=> 5x + 15 = 3(x + 15)

=> 5x + 15 = 3x + 45

=> 5x - 3x = 45 - 15

=> 2x = 30

Divide each side by 2

=> x = 15

**Step 3:**

Father's present age = 5x = 5 * 15

= 75

Hence, father is of 75 years.**answer**

Therefore father's age = 5x

(Father is 5 times his son's age)

After 15 years:

Son's age = x + 15

and father's age = 5x + 15

Father's age = Thrice the son's age

=> 5x + 15 = 3(x + 15)

=> 5x + 15 = 3x + 45

=> 5x - 3x = 45 - 15

=> 2x = 30

Divide each side by 2

=> x = 15

Father's present age = 5x = 5 * 15

= 75

Hence, father is of 75 years.