If one-half of a number is 8 less than two-thirds of the number, what is the number?

1 Answer
Nov 23, 2016

The number is #48#

Explanation:

First, let's call the number we are looking for #n#.

We can then write "two-thirds of the number" as #2/3 n#

We can also write "one-half of a number" as #1/2 n#

Finally we are told

#1/2 n# is the same as #2/3 n - 8# or:

#1/2 n = 2/3 n - 8#

We can now solve for #n#:

#1/2n - 2/3n = 2/3n - 8 - 2/3n#

#1/2n - 2/3n = -8#

We next need to get the fractions over common denominators, in this case #6# by multiplying each fraction by the necessary for of #1#:

#(3/3) 1/2n - (2/2) 2/3n = -8#

#3/6n - 4/6n = -8#

#-1/6 n = -8#

We can finally solve for #n# by multiplying by -6 to isolate #n#

#-6 * (-1/6)n = -8 * -6#

#1n = 48#

#n = 48#