You take a bulk sample from a borrow pit to your lab. Before carrying out a particular test, you

need to bring the material to exactly $9\mathrm{.}0\%$ target water content. You weight the entire sample at its

existing water content and find its total mass is $10,152$ g$.$ You take a representative subsample of

mass $146\mathrm{.}3$ g and after drying in the oven measure a dry mass of $138\mathrm{.}9$ g$.$ How much water do you

need to add to bring the bulk sample to the target water content? $($Note: please assume that the

oven$-$dried representative subsample is not returned to the larger bulk sample before adding the

required amount of water to reach the $9\mathrm{.}0\%$ target water content$).$