242 Finding the unknown two forces with given resultant

Sum of vertical forces
$R = \Sigma F_v$

$300 = -100 + P - F + 200$

$P = 200 + F$
 

Moment about point A
$Rd = \Sigma Fx$

$300(4) = -100(0) + P(2) - F(5) + 200(7)$

$1200 = 2P - 5F + 1400$

$2P - 5F + 200 = 0$

$2(200 + F) - 5F + 200 = 0$

$400 + 2F - 5F + 200 = 0$

$600 = 3F$

$F = 200 \, \text{ lb}$           answer
 

$P = 200 + 200$

$P = 400 \, \text{ lb}$           answer