Answer:
Question :-
- One number is greater than the other number by 3. The sum of the two numbers is 23. The two numbers are ?
Given :-
- One number is greater than the other number by 3.
- The sum of the two numbers is 23.
To Find :-
- What are the two numbers.
Solution :-
Let,
[tex]:\mapsto \bf First\: Number =\: a\\[/tex]
[tex]:\mapsto \bf Second\: Number =\: (a + 3)\\[/tex]
According to the question :
[tex]\bigstar[/tex] The sum of the two numbers is 23.
So,
[tex]\small :\implies \bf \bigg\{First\: Number\bigg\} + \bigg\{Second\: Number\bigg\} =\: 23\\[/tex]
[tex]:\implies \sf a + (a + 3) =\: 23[/tex]
[tex]:\implies \sf a + a + 3 =\: 23[/tex]
[tex]:\implies \sf 2a + 3 =\: 23[/tex]
[tex]:\implies \sf 2a =\: 23 - 3[/tex]
[tex]:\implies \sf 2a =\: 20[/tex]
[tex]:\implies \sf a =\: \dfrac{\cancel{20}}{\cancel{2}}[/tex]
[tex]:\implies \sf a =\: \dfrac{10}{1}[/tex]
[tex]:\implies \sf\bold{\blue{a =\: 10}}\\[/tex]
Hence, the required two numbers are :
[tex]\dag[/tex] First Number :
[tex]\dashrightarrow \sf First\: Number =\: a[/tex]
[tex]\dashrightarrow \sf\bold{\red{First\: Number =\: 10}}\\[/tex]
[tex]\dag[/tex] Second Number :
[tex]\dashrightarrow \sf Second\: Number =\: (a + 3)\\[/tex]
[tex]\dashrightarrow \sf Second\: Number =\: 10 + 3\\[/tex]
[tex]\dashrightarrow \sf\bold{\red{Second\: Number =\: 13}}\\[/tex]
[tex]\sf\bold{\purple{\underline{\therefore\: The\: two\: numbers\: are\: 10\: and\: 13\: .}}}\\[/tex]
[tex]\\[/tex]
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☆ VERIFICATION ☆Let's verify the above answer :-
[tex]\clubsuit[/tex] The sum of two numbers is 23.
[tex]\leadsto \bf a + (a + 3) =\: 23[/tex]
By putting a = 10 we get,
[tex]\leadsto \sf 10 + (10 + 3) =\: 23[/tex]
[tex]\leadsto \sf 10 + 13 =\: 23[/tex]
[tex]\leadsto \sf\bold{\pink{23 =\: 23}}\\[/tex]
[tex]\leadsto \sf\bold{\green{L.H.S =\: R.H.S}}\\[/tex]
HENCE, VERIFIED !!
[tex]\\[/tex]
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