If one-half a number is subtracted from five-sixths of the number, the difference is 6. Find the number.
Please show the work so I can learn how to do it
2006-10-21 13:43:07 · 15 answers · asked by George F 1 in Science & Mathematics ➔ Mathematics
Let X be the number...
then 5X/6 - X/2 = 6...
simple algebra from here...
multiply each term by 6 to clear fractions, and get...5X-3X=36 or 2X=36...
hence X=18
2006-10-21 14:01:50 · answer #1 · answered by L. A. L. 6 · 0⤊ 0⤋
Let this 'number' be x. Write out the an expression for the problem in terms of x. Here it is:
(5/6)x-(1/2)x = 6
(5/6)x-(3/6)x = 6
(2/6)x = 6
(1/3)x = 6
x = 18
The number you are looking for is 18. You can skip many of teh steps above to make it a two or three line solution, but since you asked for the working, there it is.
2006-10-21 13:51:26 · answer #2 · answered by Adrian W 2 · 0⤊ 0⤋
1/2 the number subtracted from 5./6 of the number is 2/6 or 1/3 of the number.
So if 1/3 of a number is 6, then what is the number?
2006-10-21 13:49:09 · answer #3 · answered by arbiter007 6 · 0⤊ 0⤋
permit the quantity = X (5/6)X - (a million/2)X = 6 till now subtracting fractions, you may desire to get a similar denominator for the two. Multiply a million/2 by way of 3/3 to get 3/6 (5/6)X - (3/6)X = 6 (2/6)X = 6 now multiply the two sodes by way of (6/2) to get- X = 6 * (6/2) = 18
2016-11-24 21:48:36 · answer #4 · answered by ? 4 · 0⤊ 0⤋
5/6X - 1/2X = 6 ::
Common Denominator = 12
(10 - 6)/12 or in lowest terms ::
(5X - 3X)/6 = 6 ::
2X/6 = 6
Remember that the (6) has a Denominator of (1)
Cross Multiply to elimimate the fraction ::
6 X 6 = 36 and 2 X 1 = 2 ::
collect the terms. ::
X = 36/2 ::
X = 18
Proof:: 5/6 X18 = 14.999
3/6 X 18 = 9
14.999 - 9 = 6 Note: 14.999 = 15
2006-10-21 15:05:02 · answer #5 · answered by Anonymous · 0⤊ 0⤋
5x/6 - x/2 = 6
Multiply both sides by 6
5x - 3x = 36
2x = 36
x = 18
the hard part is seeing that the statement
"If one-hallf a number is subtracted from 5-sixths of a number, the difference is 6"
can be said as
"Five-sixths of a number less one-half a number is 6"
which is represented by the equation I wrote.
2006-10-21 13:59:35 · answer #6 · answered by Anonymous · 0⤊ 0⤋
You need to convert to a common denominator. 1/2 = 3/6
So write your problem like this:
5/6x - 3/6x = 6
5 - 3 = 2, so 5/6 - 3/6 = 2/6.
Your problem becomes 2/6x = 6.
Multiply both sides of the equation by 6 to get rid of the fraction.
6 * 2/6x = 6 * 6
2x = 36.
Now divide both sides by 2 to solve for x.
2x/2 = 36/2
So x = 18.
Hope this helps.
2006-10-21 13:54:32 · answer #7 · answered by Valerie R 2 · 0⤊ 0⤋
5/6 x-1/2 x=5/6 x-3/6 x=2/6 x=1/3 x
1/3 x=6
x=18
2006-10-21 13:50:21 · answer #8 · answered by yupchagee 7 · 0⤊ 0⤋
18
Using 'x' for 'a number'.
5/6x - 1/2x = 6
5/6x - 3/6x = 6
multiply times 6 to rid of the fractions.
5x - 3x = 36
2x = 36
x=18
2006-10-21 13:44:49 · answer #9 · answered by merlin_steele 6 · 0⤊ 0⤋
let x be the number
one-half the number is x/2
five-sixth of the number is 5x/6
the difference (5x/6)-(x/2) = 6
multiply both sides by 6 which is lcm of 2 and 6 the denomonators in the left hand side (lhs) of the equation
you get...5x-3x = 36
so 2x = 36
so x = 18
2006-10-21 22:07:31 · answer #10 · answered by grandpa 4 · 0⤊ 0⤋