Question

I add 45 to a certain number and then divide the sum by 2.the result is five times the original number.find the original number.

Answer 1

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Answer 2

Answer:

The original number is 5.

Explanation:

Given,add 45 to a certain number.

Let the number be x.

After adding 45 to the number becomes $= x + 45$

Then divide the sum by 2

Now the number $= \frac{x + 45}{2}$

It is also given that the result is five times the original number.

So, according to question,

$\frac{x + 45}{2} = 5 \times x \\ \frac{x + 45}{2} = 5x$

By cross multiplication,

$x + 45 = 5x \times 2 \\ x + 45 = 10x$

We are separating variable and constant part,

$10x - x = 45 \\ 9x = 45 \\ x = \frac{45}{9} \\ x = 5$

So, required original number is 5.

This is a problem Equation part of Algebra.

Some important Algebra formulas:

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Equation related two more questions:

https://brainly.in/question/43712241

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