If 3 is subtracted from the numerator of a fraction, the value of the fraction is 1/2. If 6 is added to the denominator of the ORIGINAL fraction, the value of the fraction is 1/2. What is the original fraction?
(x-3)/y = .5
x/(y+6) = .5
-----------------
.5 y = x - 3
.5 y + 3 = x
these two equations are the same, choose any old x (infinite number of solutions)
if x = 13
.5 y = 10 so y = 20
x/y = 13/20
check that
(13 -3)/20 = 1/2 sure enough
(13)/(26) = 1/2 sure enough
OK, THANK YOU. But I still do not understand why x=13. that is exactly what my text uses, as well. How did you know to use 13 for x?
I just reworked it using your method and subsituted as you did. Then I used x=15 and got 15/24 for my final answer. However text says the correct answer is 13/20, does not say infinite number. I am thinking this is a book error! Anyway, thank you!
I just used 13 because I wanted easy numbers
trying x = 15 now
.5 y = 12
y = 24
so
15/24 yes
15-3/24 = 1/2 yes
15/30 = 1/2 yes
so 15/24 is just as good as 13/20
To find the original fraction, let's start by assigning variables.
Let the numerator of the original fraction be x.
Let the denominator of the original fraction be y.
According to the first condition, when 3 is subtracted from the numerator of the fraction, the value becomes 1/2. So we can form the equation:
(x - 3) / y = 1/2
According to the second condition, when 6 is added to the denominator of the original fraction, the value becomes 1/2. So we can form the equation:
x / (y + 6) = 1/2
Now we have a system of equations. To solve it, we can use the method of substitution.
Let's solve the first equation for x:
2(x - 3) = y (cross-multiply)
2x - 6 = y (distribute the 2)
Now, substitute this value of y in the second equation:
x / (2x - 6 + 6) = 1/2
x / 2x = 1/2
Now, we can cancel out the common factor of x:
1/2 = 1/2
This means that no matter what x is, the equation will be true.
So, we can say that the original fraction is x/y, where x can be any number, and y can be any number as long as it is not zero (since division by zero is undefined).
Hence, we can conclude that the original fraction cannot be determined based on the given information.