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proportion. 1
7
Example.
Eight men can finish a certain work in 12 days. Howmany
men are required to do the same work in 3 days ?
Here we see that the fewer days in which the work is to be
done, the more men are required. Therefore, this example is
in inverse proportion.
In 12 days the work was done by 8 men ; therefore, in order
to do the work in 3 days it will require -
== 32 men.
It requires 4 times as many men because the work is to be
done in one quarter of the time.
Compound Proportion.
A proportion is called compound, if to the three terms there
are combined other terms which must be taken into considera-
tion in solving the problem.
A very easy way to solve a compound proportion is to
(same as is shown in the following examples) place the con-
ditional proposition under the interrogative sentence, term
for term, and write x for the unknown quantity in the inter-
rogative sentence ; draw a vertical line ;
place x at the top at the
left-hand side ; then try term for term and see if they are direct
or inverse proportionally relative to x, exactly the same way as
if each term in the conditional proposition and the correspond-
ing term in the interrogative sentence were terms in a simple
rule-of-three problem. Arrange each term in the interrogative
sentence either on the right or left of the vertical line, according
to whether it is found to be either a multiplier or a divisor, when
the problem, independent of the other terms, is considered as a
simple rule-of-three problem.
After all the terms in the interrogative sentence are thus
arranged, place each corresponding term in the conditional
proposition on the opposite side of the vertical line. Then
clear away all fractions by reducing them to improper frac-
tions, and let the numerator remain on the same side of the verti-
cal line where it is, but transfer the denominator to the opposite
side. Now cancel any term with another on the opposite
side of the vertical line ; then multiply all the quantities on the
right side of the vertical line with each other. Also multiply
all the quantities on the left side of the vertical line with each
other.
Divide the product on the right side by the product on the
left, and the quotient is the answer to the problem.
Example 1.
A certain work is executed by 15 men in 6 days, by work-
ing 8 hours each day. How many days would it take to do the
same amount of work if 12 men are working 7j^ hours each
dav?
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