If 3 is subtracted from the numerator of a certain fraction, the value becomes 2/3. If 10 is added to the denominator of the original fraction, the value becomes 1/2. Find the original fraction.
Solve the problems by using 2 variables
HOW DO I START THIS WHAT ARE THE 2 EQUATIONS and can you label the variable like let variable x = 3x-1
i mean label the variable like let x= # of somthing
original fraction is n/d
(n-3)/d = 2/3
n/(d+10) = 1/2
3(n-3) = 2d
2n = d+10
3n - 2d = 9
2n - d = 10
n = 11
d = 12
check:
(11-3)/12 = 8/12 = 2/3
11/(12+10) = 11/22 = 1/2
To solve this problem using two variables, let's label the numerator of the original fraction as "x" and the denominator as "y".
We are given two conditions:
Condition 1: If 3 is subtracted from the numerator, the value becomes 2/3. This can be written as:
(x - 3) / y = 2/3 -----> Equation 1
Condition 2: If 10 is added to the denominator, the value becomes 1/2. This can be written as:
x / (y + 10) = 1/2 -----> Equation 2
We now have our two equations: Equation 1 and Equation 2.
To solve for x and y, we can solve these equations simultaneously by substitution or elimination methods. Would you like me to continue with one of these methods?
To start solving this problem using two variables, let's label the variables as follows:
Let the numerator of the original fraction be represented by the variable 'x'.
Let the denominator of the original fraction be represented by the variable 'y'.
Now, we can proceed to establish the two equations based on the given information:
1) "If 3 is subtracted from the numerator of a certain fraction, the value becomes 2/3":
This can be written as the equation: (x - 3) / y = 2/3.
2) "If 10 is added to the denominator of the original fraction, the value becomes 1/2":
This can be written as the equation: x / (y + 10) = 1/2.
Therefore, you have the system of equations:
(x - 3) / y = 2/3,
x / (y + 10) = 1/2.
With these two equations, we can solve for the values of 'x' and 'y', which will give us the original fraction.