# 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?

Jul 28, 2018

The bigger and smaller numbers are $42 \mathmr{and} 10$ respectively.

#### Explanation:

Let the bigger and smaller number be $b \mathmr{and} s$ 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,

$\left(b + \cancel{2 s}\right) + \left(6 b - \cancel{2 s}\right) = 62 + 232$ or

$7 b = 294 \mathmr{and} b = \frac{294}{7} \mathmr{and} b = 42$ ,putting $b = 42$ in

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

$2 s = 20 \mathmr{and} s = 10 \therefore b = 42 \mathmr{and} s = 10$

The bigger and smaller numbers are $42 \mathmr{and} 10$ [Ans]

Jul 28, 2018

$x = 10$
$y = 42$

#### Explanation:

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

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

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

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