COMPOUND PROPORTION. 127 



second stating -, and so en, as far as there are any numbers 

 in the general stating, always making the fourth number, 

 resulting from each simple stating, the second term of 

 the next. So sjiall the last resulting number be t}\^ answer 

 required. 



2. By one cperatian. — Multiply together all the terms in 

 the first place, and also all the terms in the third place. 

 Then multiply the latter product by the middle term, and 

 divide the result hj the former product j and the quo^tieut 

 \\dll be the answer required. 



Note i. It is generally best to work by the latter rheth- 

 od, viz. by one operation. And after the stating, and be- 

 fore the commencement of the operation, if one of the 

 first terms,- and either the middle t^rm, or one of the last 

 terms, can be exactly divided by one and the same number, 

 let them be divided, and the qiiotients used instead of 

 them ; which will much shorten the w^ork. 



'• Note 2. The first and third terms of each llrre, if of 

 different denominations^ must be redu(!ed to the same de- 

 nomniation. 



EXAMPLES. 



I. How many men can complete a trench of 135 yards 

 long in 8 days, provided i6men*can dig 54 yards in 6 davs ? 



General Stating. 



54 

 8 



-yds. or 2 7 ,^ fi^Syds. ore! 



y > : 16 men ;: -! ^j-' r • 



days, ar 43 [^ o days, or 33 



First Metftod. 



yds. men. yds. days. men. days. 



54>r-27=2 z : 16 :: 5 : 4 : 40 : : 5 : 



135-^27=^ 5 3 



6 -f- 2^:3 2)80(40 men. 4)120(30 men, the answer. 



8 12 



Second 



