5\12 of a number is subtracted from 3\4 of the number.their positive difference is 7 less than 5\6 of the number.find the number
Please give me the answer
3/4 x - 5/12 x = 5/6 x - 7
multiply by 12 to clear fractions, and you have
9x-5x = 10x-84
Now finish it off
5/2 of a number is subtracted from 3/4 of the number. Thier positive difference is 7 less than 5/6 of the number. Find the number
Well, well, well, looks like we've got a math problem in need of a humor solution! So, let's call this mysterious number "X" because X marks the spot, right?
Now, according to the problem, when you subtract 5/12 of X from 3/4 of X, their positive difference is 7 less than 5/6 of X. That's quite a mouthful!
So, mathematically, we can translate this into an equation:
(3/4)X - (5/12)X = (5/6)X - 7
Now, to solve this equation, we'll need to do a little mathematical magic. Let's simplify things a bit:
[(9/12)X - (5/12)X] = (5/6)X - 7
(4/12)X = (5/6)X - 7
Now, let's get rid of those pesky fractions by multiplying everything by the common denominator of 12:
4X = 10X - 84
Subtract 10X from both sides:
-6X = -84
Divide both sides by -6:
X = 14
Ta-da! The number we were searching for is 14! Now, wasn't that an amusing little adventure in math? Keep smiling and don't forget to appreciate the funny side of numbers!
Let's assume the number is represented by "x".
According to the problem statement, "5/12 of the number is subtracted from 3/4 of the number." This can be expressed as:
(3/4)x - (5/12)x
Next, we're told that "their positive difference is 7 less than 5/6 of the number." This can be expressed as:
((3/4)x - (5/12)x) - 7 = (5/6)x
Now, let's solve this equation to find the value of "x."
First, we need to simplify the equation by finding a common denominator for the fractions:
[(9/12)x - (5/12)x] - 7 = (10/12)x
Simplifying further,
(4/12)x - 7 = (10/12)x
Multiplying both sides of the equation by 12 to eliminate the denominators,
4x - 84 = 10x
Moving the variables to one side of the equation and constants to the other side,
10x - 4x = 84
6x = 84
Dividing both sides by 6,
x = 84/6
x = 14
Therefore, the number is 14.