Question

the numerator of a rational is 5 less than the denomitor. if the denominator is increased by 7 and numerator by 2, we again get the same rational number. find the number

Answer 1

Step-by-step explanation:

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Answer 2

Given - The numerator of a rational is 5 less than the denominator

Find - Number

Solution - Let the number be x.

So, original ratio is

$\frac{x - 5}{x}$

After addition of 7 in denominator and 2 in numerator, the new ratio will be -

$\frac{x - 5 + 2}{x + 7}$

Both the ratio are equal, so the equation will be -

$\frac{x - 5}{x} = \frac{x - 5 + 2}{x + 7}$

Solving the equation by performing cross multiplication -

(x-5)(x+7) = (x-5+2)(x)

Further performing multiplication -

x² + 7x - 5x - 35 = (x-3)(x)

x² + 7x - 5x - 35 = x² - 3x

Further performing addition and subtraction -

2x - 35 = - 3x

35 = 2x + 3x

35 = 5x

x = 7

Therefore, the number is 7.