If the numerator and denominator of the fractions 3/4 be increased by a certain number and those of the fraction 5/6 be decreased by the same number, the result will be the same. Find the number.
Answers
Answer:
let the required number be ' x '
first case : when the numerator and denominator of the fraction 3/ 4
increased by x
then the fraction formed
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=( 3 + x ) / ( 4 + x )
second case : when the numerator and denominator of the fraction 5 / 6 is decreased by x
then,the fraction formed
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=( 5 - x )/ ( 6 - x )
according to question , first case and second case are same . so now
( 3 + x ) / ( 4 + x ) = ( 5 - x ) / ( 6 - x )
( 6 - x ) ( 3 + x ) = ( 4 + x ) ( 5 - x )
18 + 6 x - 3 x - x^2 = 20 - 4 x + 5x - x^2
18 + 3 x = 20 + x - x^2 + x^2
18 + 3 x = 20 + x
3 x - x = 20 - 18
2 x = 2
x = 1
therefore , required number = 1
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Your Answer : 1
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Hope it will help you please mark as brainliest.
1
Step-by-step explanation:
here first we take numerator and denominator (given) (3/4) if we the unknown number x is added both in numerator and denominator we get
(3+x)/(4+x)
then if we go to another fraction (5/6)
then according to question if unknown same number x is substrate from the given fraction both in numerator and denominator
(5-x)/(6-x)
Here according to question both fractions are same then by equalling them we get x value.
(3+x)/(4+x) = (5-x)/(6-x)
Then by doing cross multiplication
(3+x)(6-x)=(4+x)(5-x)
18-3x+6x-x^2=20-4x+5x-x^2
Then we get the value of X is 1