Question

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Answer 1

QUESTION :

FIND TWO NUMBERS WHOSE SUM IS 27 AND PRODUCT IS 182 .

ANSWER :

LET THE FIRST OF THE TWO NUMBERS WHOSE SUM IS 27 BE x .

THEN , THE SECOND NUMBER IS 27 - x AND THE PRODUCT OF THOSE TWO NUMBERS IS x(27- x) .

THEIR PRODUCT IS GIVEN TO BE 182 .

$x(27 - x) = 182 \\ 27x - {x}^{2} - 182 = 0 \\ {x}^{2} - 27x + 182 = 0 \\ {x}^{2} - 14x - 13x + 182 = 0 \\ x(x - 14) - 13(x - 14) = 0 \\ (x - 14)(x - 13) = 0 \\ x - 14 = 0 \: \: or \: \: x - 13 = 0 \\ x = 14 \: \: or \: \: x = 13$

HERE , BOTH THE ANSWERS ARE ADMISSIBLE .

HENCE , IF x = 14 , IT GIVES THAT THE FIRST NUMBER = x = 14 AND THE SECOND NUMBER =27 - x = 27 - 14 = 13 .

AND IF x = 13 , IT GIVES THAT THE FIRST NUMBER = x = 13 AND THE SECOND NUMBER

= 27 - x = 27 - 13 = 14 .

• THUS , IN EITHER CASE , THE REQUIRED NUMBERS ARE 13 AND 14 .