Dog problem

Let $d_1$ be the weight of the heavier dog and $d_2$ be the weight of the lighter dog.

$d_1 - d_2 = 25$

$d_1 + d_2 = 137$

Add the equations to eliminate $d_2$ .

$2d_1 = 162$

$d_1 = 81$

p.s. $d_2 = 56$

Let the heavier dog be $\text{A}$ and the lighter dog be $\text{B}$ , then

$\text{A=25+B}$ $\Rightarrow$ $[1]$

$\text{A+B=137}$ $\Rightarrow$ $[2]$

Substituting $[1]$ in $[2]$ , we get

$\text{25+B+B=137}$

$\text{2B=112}$

$\text{B=56}$

It follows that

$\text{A=25+B=25=56=}\color{#69047E}\large\boxed{81}$