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 3/2, find the fraction.
Add an Answer
More Questions From This User See All
Copyright © 2024 EHUB.TIPS team's - All rights reserved.
Answers & Comments
Given : q = p +8 --------eq.1
When p' = p + 17 , q' = q - 1, we get
p'/q' = 3/2 = (p+17)/(q-1)
2(p + 17) = 3(q -1) = 3q - 3 = 2p + 34
3q = 2p + 31 --------------eq.2
Put eq.1 in 2, we get
3(p +8 ) = 2p + 31
3p +24 = 2p + 31
p = 7
q = 15
The fraction is 7/15
If the numerator is x then the denominator will be x + 8.
Total fraction = x/x+8. ---- (1)
Given that numerator is increased by 17 and decreased by 1, the number is 3/2.
x + 17/x+8-1 = 3/2
x + 17/x + 7 = 3/2
2x + 34 = 3x + 21
x = 13.
Substitute x = 31 in (1), we get
Fraction = 13/21.
Hope this helps!