The sum of a number and two times a smaller number is 62. Three times the bigger number exceeds the smaller number by 116. The bigger and smaller number is what?

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Answer 1 · 2018-07-28T10:50:53

The bigger and smaller numbers are $42 and 10$ respectively.

Let the bigger and smaller number be $b and s$ respectively.

By given conditions , $b+2 s=62 ; (1) and 3 b-s=116 ; (2)$

multiplying the equation (2) by $2$ we get, $6 b -2 s =232; (3)$

Adding equations (1) and (3) we get,

$(b+cancel(2 s)) + (6 b-cancel(2 s))=62+232$ or

$7 b = 294 or b= 294/7 or b= 42$ ,putting $b=42$ in

equation (1) we get , $42 +2 s=62 :. 2 s = 62-42$ or

$2 s =20 or s =10 :. b=42 and s=10$

The bigger and smaller numbers are $42 and 10$ [Ans]

Answer 2 · 2018-07-28T12:06:29

$x = 10$
$y = 42$

The sum of a number and two times a smaller number is 62
$2x + y = 62$
so $y = 62 - 2x$

Three times the bigger number exceeds the smaller number by 116
$x +116 = 3y$

substitute for $y$ :
$x +116 = 3(62 - 2x)$
$x +6x = 186 -116$
$7x = 70$
$x = 10$

$3y = 10 +116 = 126$
#y = 126/3 = 42