elmer burns works for a ready-mix concrete cmpany. elmer receives an order for 3.5 cubic yards of concrete. this mixture of concrete contains sand, cement, gravel, and water, for each pound of water, there are 5 lb of sand, 2 lb of cement, and 6 lb of gravel. find (a) the total weight of the order(in pounds), assuming a cubic yard of concrete weighs 4,000 lb, and (b) how many pounds of each ingredient are needed.
So 1# water
+ 5# sand
+ 2# cement
+ 6# gravel
Total = 14# for mix.
Total weight of the order = 3.5 Yd^3 x (4,000 lbs/1 yd^3) = 14,000 lbs.
water = 14,000 lbs x (1/14) = ??
sand = 14,000 lbs x (5/14) = ??
cement = 14,000 lbs x (2/14) = ??
etc.Check my thinking.
To find the answers to both parts (a) and (b), we need to calculate the total weight of the order and the weight of each ingredient.
(a) Total weight of the order:
First, we need to determine the weight of 1 cubic yard of concrete. Given that a cubic yard of concrete weighs 4,000 pounds, we can multiply this weight by the number of cubic yards in the order:
Weight of order = 3.5 cubic yards * 4,000 pounds/cubic yard
By multiplying these values together, we can find the total weight of the order.
(b) Weight of each ingredient:
To find the weight of each ingredient, we need to determine the weight ratio of each ingredient to the weight of water. Given that for every pound of water there are 5 pounds of sand, 2 pounds of cement, and 6 pounds of gravel, we can multiply these ratios by the weight of water in the order:
Weight of sand = 5 pounds * Weight of water
Weight of cement = 2 pounds * Weight of water
Weight of gravel = 6 pounds * Weight of water
By substituting the weight of water from part (a) into these equations, we can calculate the weight of each ingredient.