# 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

#### Answer:

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

#### Answer:

$x = 10$
$y = 42$

#### 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