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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
2
n
−
2
3
n
=
2
3
n
−
8
−
2
3
n
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
2
n
−
(
2
2
)
2
3
n
=
−
8
3
6
n
−
4
6
n
=
−
8
−
1
6
n
=
−
8
We can finally solve for
n
by multiplying by -6 to isolate
n
−
6
⋅
(
−
1
6
)
n
=
−
8
⋅
−
6
1
n
=
48
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