SOLUTION: 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.

Algebra.Com
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.

your solution is that the number is equal to 14.








Answer by MathTherapy(10552)   (Show Source): 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

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


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:



The result is 7 less than 5/6 of the number:




ANSWER: 14
RELATED QUESTIONS

5/12 of a number is subtracted from 3/4 of the number their positive difference is 7... (answered by solver91311)
three times the difference of 18 subtracted from a certain number is 5 less than the... (answered by Timnewman,lwsshak3)
there are two positive numbers. the second number is 6 less than the first number. when... (answered by stanbon)
Translate the following verbal phrases into mathematical phrases 1. 5 subtracted from y (answered by MathLover1)
What is the equation of: The difference of 7 less than a number is subtracted from twice... (answered by TimothyLamb)
can you guys help me again.... 2. Five times the first of two consecutive integers... (answered by greenestamps,josgarithmetic)
23 6 less than 5 times a number is subtracted from 3 times the number. if the result is... (answered by ptaylor)
The difference when 7 less than a number is subtracted from twice the number is 12. What... (answered by psbhowmick)
The difference when 7 less than a number is subtracted from twice the number is 12. What... (answered by dddiwakar_2004)