Chapter 1 - Measurement - Problems - Page 11: 33b

3,810.7 Extra U.S. Bushels of M&M's were shipped

Work Step by Step

First we have to find out how many bushels the customer wanted in displacement tons. Then we can figure how many extra tons we shipped if we used register tons. We are given that 1 displacement ton = 7 barrels bulk 1 register ton = 20 barrels bulk 1 barrel bulk = 0.1415 m$^{3}$ 1 m$^{3}$ = 28.378 U.S. bushels We can solve this problem by using dimensional analysis. Displacement tons desired in bushels is 73 tons * $\frac{7}{1}$$\frac{barrels bulk}{displacement ton} * \frac{0.1415}{1}$$\frac{m^3}{barrel bulk}$ * $\frac{28.378}{1}$$\frac{U.S. bushels}{m^3} = 2051.91 U.S. Bushels We can also find how many U.S. bushels we actually shipped if we used register tons. Register Tons Actually Shipped in U.S. Bushels 73 tons * \frac{20}{1}$$\frac{barrels bulk}{register ton}$ * $\frac{0.1415}{1}$$\frac{m^3}{barrel bulk} * \frac{28.378}{1}$$\frac{U.S. bushels}{m^3}$ = 5862.61 U.S. Bushels Now to find the extra amount of M&M's we shipped using register tons. We just have to subtract what we actually shipped (register tons in U.S. bushels) by what the customer desired (displacement tons in U.S. bushels. 5862.61 U.S. Bushels - 2051.91 U.S. Bushels = 3810.7 U.S. Bushels

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