Question

The difference of two numbers is 26. If the first number is 4 less than twice the second number, find the two numbers.

Answer 1

SOLUTION :

★ Given :-

• The difference of two numbers is 26.

• The first number is 4 less than twice the second number.

★ To Find :-

• The numbers = ?

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

★ Method 1 :-

Suppose,

• The first number is x

• The second number is y

❖ According to first condition,

$\bigstar \: \: \sf{ \large{ \: x - y = 26 \: \: - - - - - - > (1)}}$

❖ According to second condition,

$\bigstar \: \: \sf{ \large{ \: x = 2y - 4 \: \: - - - - - - > (2)}}$

❖ From eq. (2), putting the value of eq. (1) :-

$\bigstar \: \: \sf{ \large{ \: x - y = 26 }} \\ \\ \sf{ \large{: \implies \: (2y - 4) - y = 26}} \\ \\ \sf{ \large{: \implies \: 2y - 4 - y = 26 }} \: \: \: \\ \\ \sf{ \large{: \implies \: y - 4 = 26}} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{ \large{: \implies \: y = 26 + 4}} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{ \large{ \therefore \: \: \underline{ \: y = 30 \: }}} \: \: \: \: \: \: \:$

❖ Putting the value of y in eq. (2) :-

$\bigstar \: \: \sf{ \large{ \: x = 2y - 4 }} \\ \\ \sf{ \large{: \implies \: x =( 2 \times \underline{30})- 4}} \\ \\ \sf{ \large{: \implies \: x = 60 - 4}} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{ \large{ \therefore \: \: \underline{ \: x = 56 \: }}} \: \: \: \: \:$

• Hence, the numbers are 56 and 30.

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

★ Method 2 :-

Suppose,

• The first number is x

❖ According to first condition,

• Second number will be = x - 26

❖ According to second condition,

$\bigstar \: \: \sf{ \large{ \: x = 2(x - 26) - 4 }}$

❖ Solving the above equation :-

$\bigstar \: \: \sf{ \large{ \: x = 2(x - 26) - 4 }} \\ \\ \: \: \: \sf{ \large{: \implies \: x = (2x - 52) - 4}} \\ \\ \sf{ \large{: \implies \: x = 2x - 52 - 4}} \\ \\ \: \: \: \sf{ \large{: \implies \: x - 2x = - 52 - 4}} \\ \\ \sf{ \large{: \implies \: - x = - 56 }} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{ \large{ \therefore \: \: \underline{ \: x = 56 \: }}} \: \: \:$

$\sf{ \large{ \therefore \: \: The \: \: second \: \: number = x - 26}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \large{ = 56 - 26}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \large{ = 30}}$

• Hence, the numbers are 56 and 30.

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ANSWER :

If the difference of two numbers is 26 and the first number is 4 less than twice the second number, then the two numbers will be 56 and 30.