Answer:
one number is
25
the other number is
5
Explanation:
The problem asks for the identity of two unknown numbers.
This makes the problem one with two variables.
With two variables it is necessary to have two equations.
Let x be one number
Let y be the other number.
x
+
y
=
30
( the sum of the two numbers is 30 )
x
−
y
=
20
( The difference of the two numbers is 20)
Solving the second equation for x
x
−
y
+
y
=
20
+
y
This gives
x
=
20
+
y
Substituting this value into the first equation gives.
20
+
y
+
y
=
30
combining like terms and subtracting 20 gives
20
−
20
+
2
y
=
30
−
20
This gives
#2y = 10# Dividing both sides by #2# to isolate #y# results in
2
y
2
=
10
2
solving this gives
y
=
5
Put the value of 5 for y into either equation to find x
x
+
5
=
30
subtract 5 from both sides.
x
+
5
−
5
=
30
−
5
resulting in
x
=
25
The two unknown numbers are
5
and
25
