9. In ancient China, the following were considered equal units of weight: 1 ??? = 16 ????? = 384 ?h? Solve the following problem: Now given 1 ??? of silk costs 240 coins. Tell: given 1328 coins, how many jin of silk are obtained? Give your answer exactly in units of jin, liang, zhu, and fractions of a zhu.

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.4: Subtracting Real Numbers
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9. In ancient China, the following were considered equal units of weight:

1 ??? = 16 ????? = 384 ?h?

Solve the following problem:

Now given 1 ??? of silk costs 240 coins. Tell: given 1328 coins, how many jin of silk are obtained? Give your answer exactly in units of jin, liang, zhu, and fractions of a zhu.

Expert Solution
Step 1

Given that 

    1 jin = 16 liang = 384 zhu

 (1)      Now 1 jin of silk cost  = 240 coins

 that means    for 240 coins  =  1 jin of silk

                      for 1328 coins =  1328240=8315=5.53333  jin of silk.

(2)    Next     5.53333 jin = 384 ( 5.53333 ) zhu

                                       =106245=2124.8 zhu

                                      =212445 zhu

(3)  But 5 jin = 384 ( 5 ) = 1920 zhu

      212445 zhu - 1920 zhu = 20445 zhu

                                            =20445 ÷ 38416 liang

                                            =20445 ÷ 24 liang

                                            =8.5333 liang

                                         

 

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