Question

Sum of the digits of a two digit number is 17. If 18 is added to the original number the digits interchange their places. Write two linear equation representing these situations.

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• word problem

• Sum of two digit no is 17

• if 18 is added to the original no the digit going to interchange their place

${\sf{\green{\underline{\large{To\:find}}}}}$

• linear equations for their solution

${\sf{\pink{\underline{\Large{Explanation}}}}}$

Let the no be unit place be x and tens place be y

• Then sum of digit = 17

x + y = 17____(1)

Original no

10y + x

New number

• 10x + y

According to the question

• 18 is added to the original no the new no change thier place

10y+x+18=10x+y

=>10x-x+y-10y=18

=>9x-9y=18

=>x-y=2_____(2)

Solving equation (1) and (2)

x + y = 17

x-y=2

________

2x=19

=>x=9.5

Putting the values in Equation (1)

x + y = 17

=>9.5+y=17

=>y=7.5

Hence no is (10y+x)=(75+9.5)=84.5

Answer 2

$\red{\color{white}{\fcolorbox{cyan}{black}{Answer:-}}}$

Let the no be unit place be x and tens place be y

Then sum of digit = 17

x + y = 17⠀⠀⠀⠀⠀⠀____(i)

Original number :-

10y + x

New number :-

10x + y

According to the question :-

18 is added to the original no the new no change thier place.

10y+x+18=10x+y

10x-x+y-10y=18

9x-9y=18

x-y=2⠀⠀⠀⠀⠀⠀⠀⠀_____(ii)

Solving equation (i) and (ii) :-

x + y = 17

x-y=2

Now,

2x=19

x=9.5

Putting the values in Equation (i) :-

x + y = 17

9.5+y=17

y=7.5

Hence,

Number is (10y+x) = (75+9.5) = 84.5