SOLUTION: if 2 is added to the numerator and 3 to the denominator of a fraction. Its value will be 3/4. If 3 is subtracted from the numerator and 1 from the denominator it's value will be 1/

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: if 2 is added to the numerator and 3 to the denominator of a fraction. Its value will be 3/4. If 3 is subtracted from the numerator and 1 from the denominator it's value will be 1/      Log On


   

Question 1103256: if 2 is added to the numerator and 3 to the denominator of a fraction. Its value will be 3/4. If 3 is subtracted from the numerator and 1 from the denominator it's value will be 1/4 what is the fraction
Found 2 solutions by Theo, ankor@dixie-net.com:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x = the numerator
let y = the denominator.

the fraction you are looking for is x/y.

if 2 is added to the numerator and 3 to the denominator of the fraction, its value will be 3/4.

the equation for the fraction becomes (x+2) / (y+3) = 3/4.

If 3 is subtracted from the numerator and 1 from the denominator it's value will be 1/4.

the equation for the fraction becomes (x-3) / (y-1) = 1/4.

you have two equations that needs to be solved simultaneously.

they are:

(x+2)/(y+3) = 3/4. (first equation)

and:

(x-3)/(y-1) = 1/4. (second equation)

cross multiply the first equation of (x+2)/(y+3) = 3/4 to get:
4*(x+2) = 3*(y+3)
simplify to get:
4x+8 = 3y + 9
subtract 8 from both sides of this equation and subtract 3y from both sides of this equation to get:
4x - 3y = 1 (third equation)

cross multiply the second equation of (x-3)/(y-1) = 1/4
simplify to get:
4*(x-3) = 1*(y-1)
simplify to get:
4x-12 = y-1
subtract y from both sides of this equation and add 12 to both sides of this equation to get:
4x - y = 11 (fourth equation)

your two equations are now:

4x - 3y = 1 (third equation)
4x - y = 11 (fourth equation)

subtract the first equation from the second equation to get:
2y = 10
solve for y to get:
y = 5

go back to the third and fourth equations.

they are:

4x - 3y = 1 (third equation)
4x - y = 11 (fourth equation)

replace y with 5 in these equations to get:

4x - 15 = 1 (third equation)
4x - 5 = 11 (fourth equation)

solve for x in both equations to get x = 4.

your solution is x = 4 and y = 5.

your original fraction of x/y becomes 4/5.

if this is correct, then both original statements must be true.

first original statement is that 2 added to the numerator plus 3 added to the denominator = 3/4.

4+2 = 6 for the numerator and 5+3 = 8 for the denominator.

new fraction becomes 6/8 which is equal to 3/4.

second original statement is that 3 subtracted from the numerator plus 1 subtracted from the denominator = 1/4.

4-3 = 1 for the numerator and 5-1 = 4 for the denominator.

new fraction becomes 1/4.

both problem statements are true when x = 4 and y = 5.

solution is that the original fraction = 4/5.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation for each statement, simplify as much as possible
:
if 2 is added to the numerator and 3 to the denominator of a fraction.
Its value will be 3/4.
%28n%2B2%29%2F%28d%2B3%29 = 3%2F4
cross multiply
4(n+2) = 3(d+3)
4n + 8 = 3d + 9
4n = 3d + 9 - 8
4n = 3d + 1
If 3 is subtracted from the numerator and 1 from the denominator
it's value will be. 1/4
%28n-3%29%2F%28d-1%29 = 1%2F4
cross multiply
1(d-1) = 4(n-3)
d - 1 = 4n - 12
d = 4n - 12 + 1
d = 4n - 11
in the first simplified equation, replace d with (4n-11)
4n = 3(4n-11) + 1
4n = 12n - 33 + 1
4n = 12n - 32
32 = 12n - 4n
32 = 8n
n = 4
find d
d = 4(4) - 11
d = 5
:
what is the fraction? 4%2F5