14 is added to 2/3 of a number, the result is 1/4 times the original number. Find the number
30/7
6
6
To solve this problem, we can create an equation based on the given information.
Let's assume the number is represented by "x."
According to the problem, 14 is added to 2/3 of the number x, and the result is 1/4 times the original number.
Mathematically, this can be represented as:
14 + (2/3)x = (1/4)x
To find the value of x, we need to isolate it on one side of the equation.
To do that, we can start by subtracting (2/3)x from both sides of the equation:
14 + (2/3)x - (2/3)x = (1/4)x - (2/3)x
Simplifying the equation:
(2/3)x - (2/3)x = (1/4)x - (2/3)x
The (2/3)x cancels out, and we are left with:
14 = (1/4)x - (2/3)x
To combine the fractions on the right side, we need a common denominator. The least common denominator of 4 and 3 is 12.
We can rewrite the equation with the common denominator:
14 = (3/12)x - (8/12)x
Now we can combine the fractions on the right side:
14 = (-5/12)x
To solve for x, we can multiply both sides of the equation by the reciprocal of (-5/12), which is (-12/5):
(14)(-12/5) = (-5/12)x * (-12/5)
Simplifying further:
-168/5 = x
Therefore, the number x is equal to -168/5 or -33.6.
Note: It's important to double-check the solution to ensure it satisfies the original problem's conditions.
2/3 n + 14 = 1/4 n
8 n + 168 = 3 n