The denominator of a fraction is greater than the numerator by 8 if the numerator is increased by 17 and denominator is decreased by 1 the number obtained is 3 by 2 find the fraction
Answers
Let, the numerator of the fraction be, 'x'
The denominator is greater than the numerator by 8
So, the is denominator is = (x+8)
When the numerator gets increased by 17 then, the numerator becomes
= (x+17)
When the denominator gets decreased by 1 then the denominator becomes
= (x+8)-1
=(x+8-1)
= (x+7)
So, the new fraction obtained is = (x+17)/(x+7)
According to the problem,
(x+17)/(x+7) = 2/3
⇒ 3 × (x+17) = 2×(x+7)
[∵ When change the sides of the integers then the respective sign of the integers too gets changed such as, (+) to (-), (×) to (÷) and vice versa.]
⇒ 3x +51 = 2x +14
⇒ 3x-2x = 14-51
⇒ x = -47
So, the numerator is -47
∴ The denominator is = (-47+8)
= -39
So, the fraction is = -47/-39
= 47/39
= 1 +(8/39)
Or, 1 whole of 8/39
[∵ (+)× (+) = (+)
(-)×(-) = (+)
(+)×(-) =(-)
(-)×(+) = (-)]
Answer:
The answer is 13/21
Step-by-step explanation:
according to the equation:
x+17/x+7=3/2
upon cross multiplication:
2(x+17)=3(x+7)
=> 3x - 2x = 43-21
=> x= 13
∴ x/x+8
=> 13/13+8 = 13/21