Question

the denomitor of a fraction is 3 more than the numerator. if 5 is added to bith parts, the resulting fraction is equivalent to 4/5 . find the fraction​

Answer 1

Answer:

Let the numerator be x

Then, the denominator will be x+3

ATQ

x+5/x+3+5=4/5

x+5/x+8=4/5

5 (x+5)=4 (x+8)

5x+25=4x+32

5x-4x=32-25

x=7

Step-by-step explanation:

Answer 2

GivEn:

• The denomitor of a fraction is 3 more than the numerator.
• If 5 is added to both parts, the resulting fraction is equivalent to 4/5.

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To find:

• Find the fraction?

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Solution:

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☯ Let the numerator be x then the denominator will be (x + 3).

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$\qquad\quad\boxed{\underline{\underline{\purple{\bigstar \: \bf\: According\:to\: Question\:\bigstar}}}}$

• If 5 is added to both parts, the resulting fraction is equivalent to 4/5.

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$:\implies\sf \dfrac{(x + 5)}{(x + 8)} = \dfrac{4}{5}$

$:\implies\sf 5(x + 5) = 4(x + 8)$

$:\implies\sf 5x + 25 = 4x + 32$

$:\implies\sf 5x - 4x = 32 - 25$

$:\implies{\boxed{\sf{\pink{x = 7}}}}\;\bigstar$

Therefore,

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• Numerator of fraction, x = 7
• Denominator of fraction, (x + 3) = 10

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$\therefore$ Hence, The required fraction is 7/10.

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$\qquad\qquad\boxed{\underline{\underline{\purple{\bigstar \: \bf\: Verification\:\bigstar}}}}$

According to 1st condition:

• The denomitor of a fraction is 3 more than the numerator.

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→ 10 = 7 + 3

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According to 2nd condition:

• if 5 is added to both parts, the resulting fraction is equivalent to 4/5.

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Adding 5 to both Numerator and Denominator,

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• Numerator = (7 + 5) = 12
• Denominator = (10 + 5) = 15

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→ 12/15 = 4/5

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Hence, Proved!