Question

ALMATIANS
ODISNEY
101
CHAMP
oЯЗн
46
Mathematics VIII
2.
The difference between two numbers is 8. If2 is added to the bigger number the result
will be three times the smaller number. Find the numbers.​

Answer 1

Given :

• The difference between two numbers is 8.
• If 2 is added to the bigger number the result  will be three times the smaller number.

To find :

• Find the numbers.​

Solution :

Let the numbers be m and n.    [Where, m > n]

⇒  m - n = 8

⇒  m = n + 8

Now according 2nd condition :

⇒  m + 2 = 3n

⇒  n + 8 + 2 = 3n

⇒  10 = 3n - n

⇒  2n = 10

⇒  n = 10/2

⇒  n = 5

Now putting value of n in (i) :

⇒  m = 5 + 8

⇒  m = 13

Therefore,

Two numbers are 5 and 13 respectively.

Answer 2

Answer :

$\: \: \boxed{\boxed{\rm{\mapsto \: \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of Linear Equations in Two Variables has been used. According to this, if two unknown values are given, then we can convert them as variables and find their values using constant terms. Let's do it !!

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★ Question :-

The difference between two numbers is 8. If 2 is added to the bigger number the result will be three times the smaller number. Find the numbers.

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★ Solution :-

Given,

» The difference between two numbers = 8

» Bigger number + 2 = Smaller number × 3

• Let the smaller number be x

• Let the bigger number be y

Then according to the question :-

~ Case I :-

➺ y - x = 8

➺ y = 8 + x ... (i)

~ Case II :-

➺ y + 2 = 3x

➺ y = 3x - 2 ... (ii)

From equation (i) and (ii) , we get,

➺ 8 + x = 3x - 2

➺ 3x - x = 8 + 2

➺ 2x = 10

$\: \large{\bf{ \longmapsto \: \: x \: = \: \dfrac{10}{2}}}$

➺ x = 5

$\: \\ \boxed{\huge{\tt{x \: = \: 5}}}$

By using the value of x and equation (i), we get

➺ y = 8 + x

➺ y = 8 + 5

➺ y = 13

$\: \\ \boxed{\huge{\tt{y \: = \: 13}}}$

$\: \\ \large{\boxed{\rm{Thus, \: the \: larger \: number \: is \: \underline{\boxed{13}} \: and \: the \: smaller \: number \: is \: \underline{\boxed{5}}}}}$

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$\: \: \: \huge{\boxed{\tt{\large{More \: to \: know \: :-}}}}$

• If we draw the graph of these two lines of linear equations, we get, that both lines intersect at the coordinates (5, 13)

• Linear Equations are the the equations formed using constant and variable terms where the variable term is of single degree.