Elementary arithmetic, with brief notices of its history... by Robert Potts.

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RESULTS, HINTS, ETC., FO THIE EXERCISES.
I.
1. Art. 1. 2. The ratio is 7 to 22. 3. See Art. 2. 4. 1155. 5. A number is
called a third proportional to two numbers, when the second number forms the consequent of the first ratio and the antecedent of tile second. The third proportioral
is 26. 6. '00002928. 7. The first ratio is represented by 7, the second by ",
each of which is equal to -s. 8. 2cwt. 2clrs. 10lb. =~-r of 36cwt. lqr.
9. ~5 4s. 6d. is augmented to ~9 Os. 6d., which gives an addition of ~3 16s. This
addition on ~5 4s. 6d. gives an addition of 72-8 per cent.
II.
1. 4 tons 2cwt. lqr. 111b. =92231b. and 1121b. cost 77s. Let 92231b. cost xs.,
the prices are directly proportional to the weights, and 77=9223; ~-9223x — 7
77 =. 112 ' 11
Sometimes questions of proportion may more readily be answered by the method of
practice, as it is called, by multiplying the price of the given unit by the number of
units, and making the smaller units some aliquot part or parts of the given unit, as
in this case, lcwt. is the given unit, lqr. is I of lcwt., 71b. is ~ of lq., and 41b. is
- of lqr. If I of the price of lcwt., I of the price of lqr., and } of the price of lqr.
be added to 82 times the price of 1cwt., the same result will be obtained.
2. 2~d. 3. ~73 18s. 10fd. 4. ~19 19s. 24d. 5. 160-. 6. ~414 14s. 31d.
7. 10s. 81d. per gallon, or ~67!- per pipe. 8. ~22 8s. 9. ~741 5s. 10. If x
denote tile price of 49'31b. of bread when wheat is at 18'4s. per bushel; since the
price of 11b. of bread is directly proportional to the price of a bushel of wheat, the
X 6
proportion -49: 4: 184: 5-75 will give 18s. l-d. the price of 43-31b. of
bread. 11. 156-s.
III.
1. The simple interest is ~82 7s., and the amount ~337 7s.
2. Let ~82 7s. or 3294 sixpences=interest of 305 for x years.
~13 14s. 6d. or 549 sixpences=interest of 305 for 1 year.
Then x 3294
The1 5 r x —6 years.
3. ~13 14s. 6d. or 549 sixpences=int. of 305 for 1 year.
Let x =int. of 100 for 1 year.
x 100 20
549 305 61
x =20549 180 sixpences=~4. per cent.
61
4. ~127 or 2540s. =amount of ~100 in 6 years.
Let ~387 7s. or 7747s. =amount of x in 6 years.
m 7747 7747x100
10072540; x =_ 2540 2a~305 the principal.
IV.
1. Amount ~74 16s. Id. 2. ~11 16s. 5-.d. 3. 62 per cent. 4. 219 days is
9l=-= of 1 year. One year's interest is ~13 15s. 6d. 5. ~130. 6. ~43 6s. 8d. per