if a number is subtracted from the numerator of 3/5 and the same number is added to the denomminator of 3/5, the result is equivalent to 1. find the number
To find the number, let's set up an equation:
Let's call the number we are trying to find "x".
When x is subtracted from the numerator of 3/5, the new numerator becomes (3 - x).
And when x is added to the denominator of 3/5, the new denominator becomes (5 + x).
According to the problem, the result should be equivalent to 1. So we can set up the following equation:
(3 - x) / (5 + x) = 1
To solve this equation for x, we can start by cross-multiplying:
(3 - x) = 1 * (5 + x)
Simplifying further:
3 - x = 5 + x
Now, let's isolate the variable terms:
3 - 5 = x + x
-2 = 2x
Now divide both sides of the equation by 2 to solve for x:
-2/2 = x
-1 = x
Therefore, the number we were looking for is x = -1.
To solve this problem, let's break it down step by step:
Step 1: Understand the problem
We are given a fraction, 3/5. We are told that if we subtract a number from the numerator and add the same number to the denominator, the resulting fraction is equivalent to 1.
Step 2: Set up the equation
Let's denote the unknown number as "x". If we subtract "x" from the numerator (3) and add "x" to the denominator (5), the resulting fraction is equivalent to 1. We can write this as an equation:
(3 - x) / (5 + x) = 1
Step 3: Solve the equation
We can start by cross-multiplying to eliminate the fractions:
(3 - x) * 1 = (5 + x)
Expanding:
3 - x = 5 + x
Now, let's solve for "x":
3 + x = 5 + x
x - x = 5 - 3
0 = 2
Uh-oh! We have reached an inconsistency. The equation 0 = 2 is not true, so there is no solution to this problem.
Therefore, there is no number that satisfies the given conditions.
It helps to change to decimal form.
(.6 -n)/(.6 +n) = 1
Multiply both sides by (.6+n).
.6 - n = .6 + n
You should be able to solve it from here.