Education > Complete treatise on practical arithmetic and book-keeping

COMPOUND .PROPORTION.
37
Method of Operation.
; 1. By two operations.—Take the two tipper terms and
' re middle term, in the same order as they stand, for the
i rst stating of the Rule-of-Three; then take the fourth
lumber resulting from the first stating, for the middle
: ;rm> and the two under terms in the general stating, in
: ae same order as they stand, for the extreme terms of the
i econd stating ; and the fourth term resulting from it will
e the answer.
| 2. By one operation.—Multiply together the terms of
11'hich the one is above the other, on both sides of the
. riddle term; then, account the two products and the
.! riddle term, as they stand, the three terms of the Rule-of-
! i Three stating, and the fourth term thence resulting will be
: he answer.
r lote. It is generally best (so work by the latter method, viz. by one
; operation. And after the stating, and before commencing the ope¬
ration, if one of the two first terms, arid either the middle term or
! one of the two last terms will exactly divide by one and the same
number, let them be divided, and the quotients used instead of them;
which will much shorten the work. Thus, if the question were
to find how many men can complete a trench of 135 yards long in 8
days, it being known that 16 men can dig 54 yards in 6 days: Hav¬
ing stated the terms according to the rule, the 54 yards will stand
above the 8 days in the first place, the 16 men in the middle, and
the 135 above 6 in the last place. Then divide the 54 and 135, each
by 27, and place their quotients 2 and 5 after them : also divide the
1 8 and 6, each by 2, and place their quotients 4 and 3 after them.
Multiply then the quotients of the first two terms together, and
their product is 8 ; and multiply the quotients of the last two to¬
gether, and their product is 15; so shall 8, 16, and 15, be the 3
terms of a single stating. Of these divide the 2d term 16 by the 1st
‘ or 8, and the quotient is 2, by which multiply 15 the Sd term, and
the product is 30, the number of men required. The whole opera¬
tion is here subjoined.
yards 54,
days 8,
2 T men f 135 yards, or 5 1
4j : 16 : : 6 days, or 3 J
: SO men
8) 16 (2
15
2
Ans. 30 mem