Asked by Abhinandan Jain
The sum of the numerator and denominator of a fraction is 17. If 3 is added to the numerator, the value of the fraction will be 1. What is the fraction?
Answers
Answered by
Bosnian
n = numerator
d = denominator
The sum of the numerator and denominator of a fraction is 17 mean:
n + d = 17
If 3 is added to the numerator, the value of the fraction will be 1 mean:
( n + 3 ) / d = 1
Now you have system of two equations:
n + d = 17
( n + 3 ) / d = 1
n + d = 17
Subtract d to both sides
n + d - d = 17 - d
n = 17 - d
( n + 3 ) / d = 1
Multiply both sides by d
n + 3 = d
Subtract 3 to both sides
n + 3 - 3 = d - 3
n = d - 3
n = n
17 - d = d - 3
Add d to both sides
17 - d + d = d - 3 + d
17 = 2 d - 3
Add 3 to both sides
17 + 3 = 2 d - 3 + 3
20 = 2 d
Divide both sides by 2
10 = d
d = 10
n = d - 3 = 10 - 3 = 7
Your fraction:
7 / 10
Proof:
n + d = 7 + 10 = 17
( n + 3 ) / d = ( 7 + 3 ) / 10 = 10 / 10 = 1
d = denominator
The sum of the numerator and denominator of a fraction is 17 mean:
n + d = 17
If 3 is added to the numerator, the value of the fraction will be 1 mean:
( n + 3 ) / d = 1
Now you have system of two equations:
n + d = 17
( n + 3 ) / d = 1
n + d = 17
Subtract d to both sides
n + d - d = 17 - d
n = 17 - d
( n + 3 ) / d = 1
Multiply both sides by d
n + 3 = d
Subtract 3 to both sides
n + 3 - 3 = d - 3
n = d - 3
n = n
17 - d = d - 3
Add d to both sides
17 - d + d = d - 3 + d
17 = 2 d - 3
Add 3 to both sides
17 + 3 = 2 d - 3 + 3
20 = 2 d
Divide both sides by 2
10 = d
d = 10
n = d - 3 = 10 - 3 = 7
Your fraction:
7 / 10
Proof:
n + d = 7 + 10 = 17
( n + 3 ) / d = ( 7 + 3 ) / 10 = 10 / 10 = 1