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
Let's call the number we're trying to find "x".
First, let's set up the equation for the information given in the problem:
3/4x - 5/12x = (5/6)x - 7
To solve for x, we need to simplify this equation:
Multiplying everything by 12 to get rid of the fractions:
9x - 5x = 10x - 84
Simplifying:
4x = 84
x = 21
Therefore, the number we're looking for is 21.
well I got x = 14
check
(3/4)(14) - (5/12)(14) = (5/6)(14) - 7 ???
21/2 - 35/6 = 35/3 - 7
63/6 -35/6 = 70/6 - 7
28/6 = 70/6 - 7
-42/6 = -7
sure enough
I think
9x - 5x = 10x - 84
Simplifying:
6x = 84
x = 14
Therefore, the number we're looking for is 14.
To solve this problem, let's assume that the number we're trying to find is represented by the variable "x".
According to the problem, 5/12 of the number is subtracted from 3/4 of the number. Mathematically, this can be written as:
(3/4)x - (5/12)x
The positive difference of these two expressions is 7 less than 5/6 of the number. So we can write another equation:
(3/4)x - (5/12)x = (5/6)x - 7
Now, let's solve the equation to find the value of "x".
First, we need to simplify the equation by finding a common denominator. The common denominator of 4, 12, and 6 is 12. So, let's multiply each term by 12:
12 * ((3/4)x) - 12 * ((5/12)x) = 12 * ((5/6)x) - 12 * 7
After simplifying, our equation becomes:
9x - 5x = 10x - 84
Combining like terms, we have:
4x = 10x - 84
Next, let's isolate the "x" term by subtracting 10x from both sides:
4x - 10x = -84
Simplifying, we get:
-6x = -84
Finally, divide both sides of the equation by -6 to solve for "x":
x = (-84) / (-6)
x = 14
Therefore, the number we're looking for is 14.