Andy had 20% fewer marbles than Henry. When Andy gave 80 marbles to Henry, the number of marbles he had left was half of what Henry had. How many marbles did Andy have in the beginning?

Andy has 320 marbles while Henry has 400 marbles.
Explanation:
Although there are two people involved in this problem, we can solve it by using one variable.
Let the number of marbles that Henry has be
x
Andy has
80
%
x
and
Henry has
100
%
x
or, Andy has
0.8
x
marbles and Henry has
x
marbles
Andy now gives 80 marbles to Henry, so he has 80 fewer marbles and Andy has 80 more marbles.
Andy has
:
(
0.8
x
−
80
)
and Henry has
(
x
+
80
)
Andy now has half as many as Henry , which means that Henry has twice as many as Andy.
Don't make the mistake of doubling Henry's marbles!

He already has more than Andy, Doubling what Andy

has will be the same as what Henry has.
2
×
Andy's marbles
=
Henry's marbles
2
(
0.8
x
−
80
)
=
x
+
80
1.6
x
−
160
=
x
+
80
0.6
x
=
80
+
160

0.6
=
3
5
5
3
×
3
5
x
=
240
×
5
3
x
=
400
From our original definition of
x
we now know that Henry has 400 marbles.
Andy has
80
100
×
400
=
320
marbles

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