Question

Find the value of the smaller number if the sum of two numbers is 30 and the difference is 14.

Answer 1

Step-by-step explanation:

x+y= 30

x-y= 14

x= 22

y=8

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Answer 2

Given :-

• sum of two numbers is 30
• difference of two numbers = 14

To Find :-

• value of smaller number ?

Solution :-

Let two numbers are x and y

then according to the question,

• x + y = 30 .......(i)
• x - y = 14 .......(ii)

on adding eq.(i) and (ii)

$\bold{: \implies x + \cancel{y }+ x - \cancel{y }= 30 + 14 } \\ \\ \bold{: \implies 2 x = 44} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies x = \cancel\frac{44}{2} }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies \:x = 22 }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

now subtract eq.(ii) from (i)

$\bold{: \implies \cancel x + y - \cancel{x }+ y = 30 - 14 } \\ \\ \bold{: \implies 2y = 16}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies y = \cancel\frac{16}{2} }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies y = 8 }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

so, two numbers are 8 and 22

hence, smaller number is 8