Question

The sum of two numbers is 14 and their difference is 4. What are the two numbers?

Answer 1

Answer:

9 and 5

Step-by-step explanation:

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Answer 2

Solution:-

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$\large\to{\underbrace{\underline{\sf{Understanding\:the\:concept:-}}}}$

$\mapsto$ Here it is given in the question that the sum of two numbers is 14 and their difference is 4. Now the question has asked us to find out the two numbers. So to find the two numbers first we will form an equation according to the question then by solving that equation we will get the 1st number and to find the second one follow the steps given.

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ANSWER:-

⪼ The first number is 9.

⪼ The second number is 5.

GIVEN:-

➤ Sum of the numbers = 14

➤ Difference of the numbers = 4

TO FIND:-

• Here we have to find out both the numbers.

SOLUTION:-

• Here we simply have to form an equation and then solve it.
• Let the first number be x.
• Let the second number be x - 4.
• By solving the equation given below we will get x.
• Once we will get x then by subtracting 4 from x we will get the 2nd number.

We know that the equation will be:-

$\underline{\boxed{\rm \bigstar Equation = 14 = x + (x - 4)}}$

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Let's solve it!

• Finding the value of x:-

$\dashrightarrow \sf{14 = x + (x - 4)}$

$\dashrightarrow \sf{14 = x + x - 4}$

$\dashrightarrow \sf{14 = 2x - 4}$

$\dashrightarrow \sf{Transposing \: 4 \: to \: L.H.S.}$

$\dashrightarrow \sf{14 + 4 = 2x}$

$\dashrightarrow \sf{18 = 2x}$

$\dashrightarrow \sf{Transposing \: 2 \: to \: L.H.S.}$

$\dashrightarrow \sf{\dfrac{18}{2} = x}$

$\dashrightarrow \sf{\dfrac{\not{18}}{\not{2}} = x}$

$\dashrightarrow \sf{\dfrac{9}{1} = x}$

$\dashrightarrow \sf{9 = x}$

$\overline{\boxed{\rm \dag \: x = 9}}$

Thus, the 1st number is 9.

• Finding the 2nd number:-
• According to the question the difference of the numbers is 4.

So,

$\dashrightarrow \sf{9 - 4}$

$\dashrightarrow \sf{9 - 4 = 5}$

$\overline{\boxed{\rm \dag \: 5}}$

Thus, the 2nd number is 5.

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VERIFICATION:-

• There are 2 methods which we will use to verify.

• By Sum:-

$\to \sf{Sum = 1st \: no. + 2nd \: no.}$

$\to\sf{9 + 5}$

$\to \sf{9 + 5 = 14}$

$\to \bm{14}$

Hence, verified.

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• By Difference:-

$\to \sf {difference = 1st \: no. - 2nd \: no.}$

$\to \sf{9 - 4}$

$\to \sf{9 - 5 = 4}$

$\to \bm{4}$

Hence, verified.

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