What was the weight of concrete in pounds per cubic foot?

Use direcly definition of density

$$ bar {d }= frac{Total, Weight}{Total, Volume} $$

$$=dfrac {W_1+ W_2+W_3 +W_4}{ dfrac{W_1}{d_1} + dfrac{W_2}{d_2} + dfrac{W_3}{d_3} +dfrac{W_4}{d_4} }$$

that would give you after needed plug-ins as $ 153 dfrac{lbs}{ft^3}.$

The mass of a batch is presumably about $200+350+94+5times 8.34$ pounds

The volume of a batch is presumably about $frac{200}{2.65 times 8.34}+ frac{350}{2.65 times 8.34}+ frac{94}{3.10 times 8.34}+5$ US gallons or about $frac{200}{2.65 times 62.4}+ frac{350}{2.65 times 62.4}+ frac{94}{3.10 times 62.4}+ frac{5}{7.48}$ cubic feet

So a batch weighs about $685.7$ pounds and has a volume of about $4.48$ cubic feet so dividing one by the other gives about $153$ pounds per cubic foot

This would be rather easier in metric units

Note that

• volume $V=5cdot 0.13+frac{550}{2.65cdot 62.4}+frac{94}{3.10cdot 62.4}=4.46 ,ft^3$

• weight $W=5cdot 0.13cdot 62.4+550+94=684.56 ,lbs$

thus

• $frac W V=153.4 ,lbs/ft^3$

I am puzzled as to why you have the weight of cement only in the numerator as well as adding it to the other weights in the denominator. To find the "weight per cubic foot" of concrete you need to divide the total weight of concrete by its volume. The total weight is 350+ 94+ 40= 484 pounds (for the water, 5 gallons is 40 pints and "a pint's a pound the world around"). Now use the specific gravities to determine the volume of each part and add them to find the total volume.