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A ton is a measure of volume frequently used in shipping, but that use requires some care because there are at least three types of tons: A displacement ton is equal to 7 barrels bulk, a freight ton is equal to 8 barrels bulk, and a register ton is equal to 20 barrels bulk. A barrel bulk is another measure of volume: 1barrelbulk=0.1415m3. Suppose you spot a shipping order for 鈥73 tons鈥 ofM&Mcandies, and you are certain that the client who sent the order intended 鈥渢on鈥 to refer to volume (instead of weight or mass, as discussed in Chapter 5). If the client actually meant displacement tons, how many extra U.S. bushels of the candies will you erroneously ship if you interpret the order as (a) 73 freight tons and (b) 73 register tons? (1m3=28.378U.S. bushels.)

Short Answer

Expert verified

(a). When the order is interpreted as 73 freight tons, the extra U.S. bushels are 293 U.S. bushels.

(b). When the order is interpreted as 73 register tons, the extra U.S. bushels are 3.81103U.S.bushels.

Step by step solution

01

Given data

1displacementton=7barrelbulk1freightton=8barrelbulk1registerton=20barrelbulk

02

Understanding the conversion factor

Unit conversion is the conversion between different units of measure for the same quantity, usually through multiplier conversion factors. Here, displacement ton, freight ton, register ton and barrel bulk and bushels are the different units for the quantity volume.

03

Determination of the number of U.S. bushels for displacement ton

To calculate the number of extra U.S. bushels, you must first convert all the tons into their equivalent U.S. bushels.

1m3=28.378U.Sbushels1barrelbulk=0.1415m3=0.1415m328.378U.Sbushel1m3=4.0155U.Sbushel

Therefore, 1barrelbulkis equivalent to 4.0155U.Sbushel.

1displacementton=7barrelbulk=7barrelbulk4.0155U.Sbushels1barrelbulk=28.108U.Sbushel

Therefore, 1displacementton is equivalent to 28.108U.Sbushel.

04

Determination of the number of U.S. bushels for freight ton

Now, use the relationship between freight ton and barrels bulk to find the relationship between freight ton and U.S. bushels.

1freightton=8barrelbulk=8barrelsbulk4.0155U.Sbushels1barrelbulk=32.124U.Sbushels

Therefore, 1freighttonis equivalent to 32.124U.Sbushels.

05

Determination of the number of U.S. bushels for a registered ton

Now, use the relationship between register ton and barrels bulk to find the relationship between register ton and U.S. bushels.

1registerton=20barrelbulk=20barrelbulk4.0155U.Sbushels1barrelbulk=80.31U.S.bushels

Therefore, 1registerton is equivalent to 80.31U.S.bushels
.

06

(a) Determination of the extra U.S. bushels when interpreted as freight tons.

The extra U.S. bushels can be given as:

Extrabushels=73(freighttons-displacementtons).

Substitute the values in the above expression.

Extrabushels=73(32.124U.S.bushels-28.108U.S.bushels)=293.168U.S.bushles293U.S.bushles

Thus, when the order is interpreted as 73 freight tons, the extra U.S. bushels are 293 U.S. bushels.

07

(b) Determination of the extra U.S. bushels when interpreted as register tons

The extra U.S. bushels can be given as:

Extrabushels=73(freighttons-displacementtons)

Substitute the values in the above expression.

Extrabushels=73(80.31U.S.bushels-28.108U.S.bushels)=3810.74U.S.bushles3.81103U.S.bushles

Thus, when the order is interpreted as 73 register tons, the extra U.S. bushels are 3.81103U.S.bushles.

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