Question

Hello everyone ✌

a) Two-third of a number when added to 6 gives 9. Find the number.
OR
b) The sum of two consecutive integers is 43. Find the two numbers.


Thanks !​

Answer 1

$\huge {\underbrace{ \sf{ \green{Answer - 1}}}}$

⭕Given:-

• Two-third of a number when added to 6 gives 9.

⭕To Find:-

• Find the number.

⭕Analysis:-

Here, a word equation is given. We will have to first convert it in mathematical equation and then solve. Let the number be x.

➜Required Equation:-

$\leadsto \sf \purple{ { \large \frac{2}{3}} x + 6 = 9}$

$\implies \sf { \large \frac{2}{3}}x = 9 - 6$

$\implies \sf { \large \frac{2}{3}}x = 3$

$\implies \sf { \large 2x = 3 \times 3 }$

$\implies \sf { \large 2x = 9 }$

$\implies \sf { \large x = \frac{9}{2} }$

$\implies \sf \orange { \large x = 4.5 }$

⭕Final Answer:-

The number is 4.5.

$\huge\purple { - - - - - - }$

$\huge {\underbrace{ \sf{ \green{Answer - 2}}}}$

⭕Given:-

• The sum of two consecutive integers is 43.

⭕To Find:-

• Find the two numbers.

⭕Analysis:-

Here, we have got two numbers, and those numbers are consecutive. Their sum is 43. It means when we will add both, we will get 43 as sum. So, the two numbers will be-

• x
• x+1

Now, we will form an equation and find our answer!

➜Required Equation:-

$\leadsto \sf \purple {x + x + 1 = 43}$

$\implies \sf {2x + 1 = 43}$

$\implies \sf {2x = 43 - 1}$

$\implies \sf {2x = 42}$

$\implies \sf {x = \frac{42}{2} }$

$\implies \sf \orange {x = 21 }$

⭕Final Answer:-

So, the two numbers will be-

• x = 21
• x+1 = 21+1 = 22

⭕ Verification:-

$\implies\sf {x + x + 1 = 43}$

$\implies\sf {21 + 22 = 43}$

$\implies\sf {43= 43}$

➜L.H.S = R.H.S

➜HENCE, VERIFIED✔️

$\huge\purple { - - - - - - }$