The Jackson standard. [volume] (Jackson C.H., Ohio) 1847-1888, 1869-04-01
ArithmeticaI Questions and

ArithmeticaI Questions and
Answers.
d, Mackley Esq. .-As / have never
seen any answer to Chromo's question
how far from Canton to Dunkirk,-
published March 4th, and il being very
simple, / thought l would send you the
answer, which is 152 miles, b travelling
s days, 8 miles per day, A travelling
u Al days, miles per day.
BELTENEBRos.
WASHINGTON IT,, March %
D. MAcKLEY Dear Sir My an
swer to the last question proposed by
De Soto is, John dug 46H bus.
A. and B. dig ditch for S1OO, one
hundred yards long, A. commencing at
one end and B. at the other. AS end
is 12 per cent. harder than BIS. How
far must each dig so as to divide the
money equally? Yours, hastily.
BETBoNEBRos.
If the tail Of COW weighs 8 3-4 lbs,
the head as much as tail and legs, the
legs 10 Of the head and tail, and the
body IA SO the weight of the head,
tail, and legs? What is the weight of
the COW? DE SoTo.
If man 6 feet in height would walk
once around the earth on the equator,
how much farther would his head move
than his feet?
Solution to A. RS "7ree and Vine ques-
ton giren in the STANDARD of Feb l8. .
The tree is 81 feet high, and grows
at the rate of 8 feet per year. The
vine rises 12 feet ,....
The vine gains 8 feet on the tree in
one year, and to gain 81 feet it will re-
quire as many years as 9 is confined
times in 81: 37-9=4 10 3x41-9
=l2 1-3. 37+12 1-3=49 1-3.
The diameter of the tree when it is
40 1-3 feet high is 16 20 inches To
find the length of the vine assume the
tree to be in the form of a cylinder:
The mean diameter is 1-9n.
HeHce-Mean circumference is 25'4S1S In.
The vine in making one circuit trav-
els distance corresponding to the
hypotenuse of right angled triangle
the sides of which are 4S inches and
rs. 1918 inches.
4S 2+25 1918 2=2953 32213124. 52958 s221S124=
54.3l44. 5l,8444x1216-67O. 276l n.==55 $3.50 #.
The height of tree will be 40 1-3 #.
Height of vine will be 55 $3.50 #.
J. M. PARKS.
EDITOR STANDARD The answer
gave to the 500, 900 question was CON-
pleted at compound interest. Not
having the paper by me when l solved
the example l made the mistake.
will now give my method of solving
the example. One dollar at 6 per cent
simple interest for 5, s, 10 and II years
will amount to 81. 80, S48, SLIGO and
$1.72 respectively. Find the least
common multiple by each number re-
spectiyely, and take such a part Of
$4,000, as each quotent is part of
the sum of the quotients.
This gives the first answer. S..
8O9 665, $6,096.935, $4,7l4665, and
| $4, 4,395755. Each Of these sums at in
terest for s, 8, 1Oand y years, amounts
to 81, ,5l3,46
SOLUTION TO THE OTHER QUESTION
The average price was 81. Consid-
ering the sheep, (which were below the
average, and the cattle, which were
above it, we find by allegation that tc
make the average price 81, TO every
head of cattle l8 sheep must have beer
bought; and for head of cattle 9(
sheep. One hog and sheep (Which
cost the average price of $1) will make
up the given number, 100, while The
average price will still be preserved
Hence the answer is "a sheep, ! hog,
and cattle.
d, MAcKLEY, Eso:-The following
| 10 my uhoWVlS w pOluC VI IHS NSuesJlUne
in last weeks STANDARD; No. by D
d. Evans, answer $558. 40 5-s. No.
by d. d. E 90 miles l. furlong, 19
rods 6 inches. By Chrome :-Consid.
Grating the fence to be straight, and moi
allowing any lap 500, 800 acres or 8;
miles square will fulfil the conditions O
the problem. BY De Soto John get
l-3 and his employer 2-3, then l-3 o
the whole minus 9 equals 1-5 of g.;
after 8 plus 5 is taken away, then B.;
of the whole minus As equals S-3 minus
IA, from which 2-3 equals 81 and J.;
equals Is l-2 bushels, (John's share)
and the number of bushels he due
equals 46 l-2 ]. L. SYLVESTER.