The average of two numbers is 50. Their difference is 40, how do you write an equation that may be used to find x the smallest of the two numbers?
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Explanation:
You know that you need to find two numbers,
x
and let's say
y
.
The average of two numbers is equal to their sum divided by
2
, so your first equation will be
x
+
y
2
=
50
The difference between
y
and
x
, since
x
is the smallest of the two, is equal to
40
, which means that your second equation will be
y
−
x
=
40
You thus have a system of two equations
{
x
+
y
2
=
50
y
−
x
=
40
To solve for
x
, use the first equation to express
y
as a function of
x
x
+
y
2
=
50
⇔
x
+
y
=
100
⇒
y
=
100
−
x
Plug this into the second equation to get
(
100
−
x
)
−
x
=
40
100
−
2
x
=
40
→
this is the equation that will get you
x
.
The value of
x
will be
2
x
=
60
⇒
x
=
30
The value of
y
will be
y
=
100
−
30
=
70
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