Question

if the sum of the difference of two number is 35 and 7 respectively find them

Answer 1

The first thing to do in algebraic equations is to assign variables to what you don't know. In this case, we don't know either number so we'll call them
x
and
y
.

The problem gives us two key bits of info. One, these numbers have a difference of
7
; so when you subtract them, you get
7
:
x
−
y
=
7


Also, they have a sum of
35
; so when you add them, you get
35
:
x
+
y
=
35


We now have a system of two equations with two unknowns:
x
−
y
=
7

x
+
y
=
35


If we add them together, we see we can cancel the
y
s:
X
x
−
y
=
7

+
x
+
y
=
35
−−−−−−−−−−
X
2
x
+
0
y
=
42

→
2
x
=
42


Now divide by
2
and we have
x
=
21
. From the equation
x
+
y
=
35
, we can see that
y
=
35
−
x
. Using this and the fact that
x
=
21
, we can solve for
y
:
y
=
35
−
x

→
y
=
35
−
21
=
14


So the two numbers are
21
and
14
, which do indeed add to
35
and have a difference of
7
.

Hope this will help you.... ✌