the denominator of a fraction is 3 less than twice the numerator. if the numerator is doubled and the denominator by 8, the resulting would be 2/3. find the original fractions
and the denominator by 8, ...
What does that mean? increase, multiplied, or what?
To solve this problem, let's set up equations based on the given information.
Let's start by assigning variables:
Let the numerator of the fraction be represented by "n".
Let the denominator of the fraction be represented by "d".
According to the first statement, the denominator is 3 less than twice the numerator:
d = 2n - 3
Next, we are told that if the numerator is doubled (2n) and the denominator is increased by 8 (d + 8), the resulting fraction is 2/3:
(2n) / (d + 8) = 2/3
Now, we have a system of two equations:
1) d = 2n - 3
2) (2n) / (d + 8) = 2/3
We can solve this system of equations using substitution or elimination to find the values of "n" and "d".
Let's solve it using substitution:
Substitute the value of "d" from equation 1) into equation 2):
(2n) / (2n - 3 + 8) = 2/3
(2n) / (2n + 5) = 2/3
Cross-multiply:
3(2n) = 2(2n + 5)
6n = 4n + 10
6n - 4n = 10
2n = 10
n = 10 / 2
n = 5
Now that we have found the value of "n" as 5, we can substitute it back into equation 1) to find the value of "d":
d = 2(5) - 3
d = 10 - 3
d = 7
Therefore, the original fraction is 5/7.
So, the original fraction is 5/7.