Question

If the same number is added to the numerator and denominator of the rational number 3/5 ,the resulting rational number is 4/5 find the number added to the numerator and denominator

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Answer 1

x = 5. The number added to the numerator and to the denominator is 5.

Explanation:

Lets start with 3/5. We're going to add the same number to the top and the bottom. We don't know that number, so we use x.

(3+x)/(5+x)

They said that then becomes 4/5.

(3+x)/(5+x) = 4/5

crossmultiply.

5(3+x) = 4(5+x)

use distributive property.

15 + 5x = 20 + 4x

subtract 4x from both sides.

15 + x = 20

subtract 15 from both sides.

x = 5

Check:

(3+5)/(5+5)

= 8/10

= 4/5