Answer: The numbers are 4 and 6.
Step-by-step explanation:
Let one number be represented as
x
and the other as
y
.
According to the problem:
x
=
2
3
y
and
x
+
y
=
10
From the second equation we get:
x
+
y
=
10
∴
y
=
10
−
x
(subtracting
x
from both sides)
Replacing the value of
y
in the first equation we get:
x
=
2
3
y
x
=
2
3
(
10
−
x
)
Multiplying both sides by
3
we get:
3
x
=
2
(
10
−
x
)
Opening the brackets and simplifying we get:
3
x
=
20
−
2
x
Add
2
x
to both sides.
5
x
=
20
Divide both sides by
5
.
x
=
4
Since from the second equation we have:
x
+
y
=
10
substituting
x
with
4
we get:
4
+
y
=
10
Subtract
4
from both sides.
y
=
6
Answer: The smaller number is 12.
Step-by-step explanation:
Just took the test
