One number is greater than the other number by 3. The sum of the two number is 23. The two numbers are?​

Answer:

• One number is greater than the other number by 3. The sum of the two numbers is 23. The two numbers are ?

• One number is greater than the other number by 3.
• The sum of the two numbers is 23.

• What are the two numbers.

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]

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

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]

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃