Question 1197889: 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. Found 3 solutions by Theo, MathTherapy, greenestamps:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! let x be the number.
3/4 * x -5/12 * x = 5/6 * x - 7.
3/4 * 3/3 = 9/12
5/6 * 2/2 = 10/12
equation becomes:
9/12 * x - 5/12 * x = 10/12 * x - 7
subtract 10/12 * x from both sides of the equation to get:
9/12 * x - 5/12 * x - 10/12 * x = - 7
combine like terms to get:
-6/12 * x = -7
multiply both sides of this equation by -12/6 to get:
x = -7 * -12/6
simplify to ge t:
x = 84/6 = 14
to confirm, replace x with that and evaluate the original equation.
you will get:
3/4 * x -5/12 * x = 5/6 * x - 7. becomes:
3/4 * 14 - 5/12 * 14 = 5/6 * 14 - 7
since 3/4 = 9/12 and 5/6 = 10/12 and 7 = 84/12, you get:
9/12 * 14 - 5/12 * 14 = 10/12 * 14 - 84/12
subtract 10/12 * 14 from both sides of the equation to get:
9/12 * 14 - 5/12 * 14 - 10/12 * 14 = -84/12
factor out the 14 on the left side of the equation to get:
14 * (9/12 - 5/12 - 10/12) = -84/12 which becomes:
14 * (-6/12) = -84/12 which becomes:
-84/12 = -84/12 which is true.
this confirms the value of x is good.
another way is to use your calculator on the original expressions on each side of the equal sign after replacing x with 14.
you will get:
3/4 * 14 - 5/12 * 14 = -4.666666.....
5/6 * 14 - 7 = -4.66666.....
since the expression on the left side of the equal sign is equal to the expression on the right side of the equal sign, the equation is true and the value of x is good.
You can put this solution on YOUR website!
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 the number be N
We then have:
9N - 5N = 10N - 84 ------ Multiplying by LCD, 12
4N - 10N = - 84
- 6N = - 84
Number or
Here is one of many alternative methods for solving the problem; this one breaks the solution into two steps, as opposed to the "standard" setup using a single equation to represent the whole problem.
Subtract 5/12 of the number from 3/4 of the number:
