Question

Sum of two number is 45 and the greater number is twice the smaller number. Then, find the numbers​

Answer 1

Answer:

15 . please mark me as brain list

Answer 2

Step-by-step explanation:

Analysis :-

$\: \: \: \:$ In this question we're given with the sum of two numbers and the greater number is twice the smaller number. And, we're asked to find out the numbers, respectively.

• The sum of two numbers is 45.
• The first number is twice the second number.

Understanding The Concept :-

$\: \: \: \:$ To find the numbers, firstly, let us assume the value of second number be "x". So that the value of the first number will be "2x", since first number is twice the second number.

As through the given data provided in the question, we know that the sum of the two numbers is 45, hence the equation so formed is,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\underbrace{\boxed{\sf{2x\ +\ x\ =\ 45}}}_{\tiny\blue {\sf{Required\ equation}}}}$

Solution :-

By solving the equation, we can obtain the value of "x". After having the value of x, we will confirm the value of x by verifying it. And to get the numbers, we simply put the value of x in the assumed numbers, and will get our final numbers. Let's do it !

Calculations :-

➲ Finding the value of x :

$\: \: \: \:$ This calculation can be carried out by solving our required equation, that is, 2x + x = 45.

$\tt \longmapsto {2x\ +\ x\ =\ 45} \\ \\ \sf \longmapsto {3x\ =\ 45} \\ \\ \sf \longmapsto {x\ =\ \dfrac{45}{3}} \\ \\ \sf \longmapsto {x\ =\ \dfrac{\cancel 3 \times 15}{\cancel 3 \times 1}} \\ \\ \sf \longmapsto {x\ =\ \dfrac{\cancel {15}}{\cancel {1}}} \\ \\ {\underbrace{\boxed{\sf{\pink{x\ =\ 15.}}}}_{\tiny\blue {\sf{Value\ of\ x}}}}$

Now, we've the value of x, that is, 15. So, before proceeding to the next step in finding the numbers, let us confirm the value of x by verifying it.

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$ ✦ Verification ✦

$\tt \longmapsto {2x\ +\ x\ =\ 45} \\ \\ \sf \longmapsto {2(15)\ +\ 15\ =\ 45} \\ \\ \sf \longmapsto {2 \times 15\ +\ 15\ =\ 45} \\ \\ \sf \longmapsto {30\ +\ 15\ =\ 45} \\ \\ {\underbrace{\boxed{\sf{\pink{45\ =\ 45}}}}_{\tiny\blue {\sf{Hence,\ Verified}}}}$

Now, the value of x is verified as the LHS is equal to the RHS. Hence, the value of x is correct.

$\: \: \: \:$ Now, we'll find out the numbers. This can be done by substituting the value of x in the assumed numbers.

➲ Finding numbers :

$\tt \longmapsto {1^{st}\ number\ =\ 2x} \\ \\ \sf \longmapsto {2(15)} \\ \\ \sf \longmapsto {2 \times 15} \\ \\ {\underbrace{\boxed{\sf{\red{30}}}}_{\tiny\blue {\sf{First\ number}}}}$

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$\tt \longmapsto {2^{nd}\ number\ =\ x} \\ \\ {\underbrace{\boxed{\sf{\red{15}}}}_{\tiny\blue {\sf{Second\ number}}}}$

By solving the formed equation we get the numbers as 30 and 15. Hence, the required numbers are 30 and 15 respectively.