Conservation of Mass Problem

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What is the weight of the final batch of mud? Class Problem: A batch of masonry cement is made by mixing three 5-gallon buckets of wet sand with one 70 lb bag of masonry mix and 3 gallons of water. The sand used in the mix is partially wet, containing an unknown amount of water. If the final batch of “mud” contains 11.3% water when the desired consistency is reached, then how many gallons of water did the sand used in the mixture contain? Assume wet sand and dry sand occupy the same volume. What is the weight of the final batch of mud? Convert all gal values to lb: Weight of 3 gal Water: 3𝑔𝑎𝑙∙8.33 𝑙𝑏𝑠 𝑔𝑎𝑙 =24.99𝑙𝑏 70 lbs masonry mix 100% masonry mix Weight of Dry Sand: 15𝑔𝑎𝑙∙0.1337 𝑓𝑡 3 𝑔𝑎𝑙 ∙111 𝑙𝑏 𝑓𝑡 3 =222.6𝑙𝑏 Wet Sand 3 - 5gal buckets = 15gal 3gal water 100% water Apply Conservation of Mass Equations: 𝑚 𝑖𝑛 − 𝑚 𝑜𝑢𝑡 + 𝑚 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 − 𝑚 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑑 = 𝑚 𝑓𝑖𝑛𝑎𝑙 − 𝑚 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 222.6lb dry sand X lb water 24.99 lb water Y lbs “mud” 11.3% water a% sand b% masonry mix 𝑚 𝑖𝑛 = 𝑚 𝑜𝑢𝑡 overall: 𝑚 𝑖𝑛 = 𝑚 𝑜𝑢𝑡 sand: X+222.6𝑙𝑏+70𝑙𝑏+24.99𝑙𝑏=Y 222.6𝑙𝑏=aY Useful Information/Conversions: Density of water = 8.33 lbs/gal Density of dry sand = 111 lbs/ft3 1 gal = 0.1337 ft3 𝑚 𝑖𝑛 = 𝑚 𝑜𝑢𝑡 water: 𝑚 𝑖𝑛 = 𝑚 𝑜𝑢𝑡 mix: X+24.99𝑙𝑏=0.113Y 70𝑙𝑏=bY

𝑚 𝑖𝑛 = 𝑚 𝑜𝑢𝑡 water: 𝑚 𝑖𝑛 = 𝑚 𝑜𝑢𝑡 overall: a. How many gallons of water did the sand used in the mixture contain? 70 lbs masonry mix 100% masonry mix 𝑚 𝑖𝑛 = 𝑚 𝑜𝑢𝑡 water: 𝑚 𝑖𝑛 = 𝑚 𝑜𝑢𝑡 overall: Wet Sand 3 - 5gal buckets = 15gal 3gal water 100% water X+24.99𝑙𝑏=0.113Y X+222.6𝑙𝑏+70𝑙𝑏+24.99𝑙𝑏=Y 222.6lb dry sand X lb water X+24.99𝑙𝑏 0.113 =Y X+222.6𝑙𝑏+70𝑙𝑏+24.99𝑙𝑏= X+24.99𝑙𝑏 0.113 Y lbs “mud” 11.3% water a% sand b% masonry mix X+317.59𝑙𝑏= X+24.99𝑙𝑏 0.113 0.113(X+317.59𝑙𝑏)=X+24.99𝑙𝑏 0.113X+35.888=X+24.99𝑙𝑏 10.898𝑙𝑏=0.887X X=12.286𝑙𝑏∙ 𝑔𝑎𝑙 8.33𝑙𝑏 =1.475𝑔𝑎𝑙 X=12.286𝑙𝑏 of water in wet sand b. What is the weight of the final batch of mud? X+24.99𝑙𝑏=0.113Y 12.286𝑙𝑏+24.99𝑙𝑏=0.113Y Useful Information/Conversions: Density of water = 8.33 lbs/gal Density of dry sand = 111 lbs/ft3 1 gal = 0.1337 ft3 37.276=0.113Y 37.276 0.113 =Y 𝑌=329.876𝑙𝑏 final batch of mud