Question

Q31) If sum of two integers is 67 and one of them is -36, find the other integer.

Answer 1

$\begin{gathered}\begin{gathered}\bf \: Given - \begin{cases} &\sf{sum \: of \: integers \: be \: 67} \\ &\sf{one \: of \: the \: integer \: is \: - 36} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: To\: find - \begin{cases} &\sf{other \: integer}  \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

• Let the other integer be 'x'.

• One of the integer = - 36

• Sum of the integers = 67

$\large \underline{\tt \: \red{ According \: to \: statement }}$

$\tt \longmapsto\: - 36 + x = 67$

$\rm :\implies\:x = 67 + 36$

$\rm :\implies\:\:\boxed{ \green{ \bf \: x = 103}}$

Additional Information :-

Properties of Integers

• Integers have 5 main properties of operation which are:

Closure Property

• Sum or difference of two integers is always integer

• closure property under addition and subtraction states that the sum or difference of any two integers will always be an integer i.e. if x and y are any two integers, x + y and x − y will also be an integer.

Associative Property

Let x, y and z be any three integers, then

• ⇒ x + (y + z) = (x + y) +z
• ⇒ x × (y × z) = (x × y) × z

Commutative Property

Suppose, x and y are any two integers, then

• ⇒ x + y = y + x
• ⇒ x × y = y × x

Distributive Property

This can be represented for any integers x, y and z as:

• ⇒ x × (y + z) = x × y + x × z
• ⇒ x × (y − z) = x × y − x × z

Identity Property

For any integer x,

• x + 0 = x = 0 + x

For any integer x,

• x × 1 = x = 1 × x