A built$-$up beam is constructed by nailing seven boards together as shown. The nails are equally spaced along the beam, and the beam supports a vertical load. As proved in mechanics of materials, the shearing forces exerted on the nails at $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ are proportional to the first moments with respect to the centroidal $\backslash ($ x $\backslash )$ axis of the red$-$shaded areas shown, respectively, in parts $($a$)$ and $($b$)$ of the figure. Knowing that the force exerted on the nail at $\backslash ($ A $\backslash )$ is $130$ N $,$ determine the force exerted on the nail at $\backslash ($ B $\backslash ).$

$($a$)$