Elements of Arithmetic, Theoretical and Practical

PROMISCUOUS QUESTIONS.

1. The sides of two square pieces of ground, are as 3 to 5, and the sum of their superficial content is 30600 square feet; what is the length of the sides of each?

Ans. 90 feet and 150 feet.

2. Three young men entering into partnership, agree to make a common stock, to which each shall contribute in the ratio of the sum of the ages of the two other partners. A is 24 years old, B 27 years, and C 31 years; what will be the share of each?

3. A parcel of tobacco is sold, some at 12 cents per pound, the rest at 15 cents per pound; the proportion of the first to the latter, was as to, and the amount of the sale $330; how many pounds were there of each kind? Of the first, 1500 lbs. 1333 lbs.

Ans. Of the 24,

4. A grocer bought coffee, 3 bags of 80 lbs. at 21 cents per lb., 6 bags of 58 lbs. at 24 cents per lb., and 9 bags of 90 lbs. each, at 18 cents per lb., and sold the whole together at 22 cents the pound; what did he make by it? Ans. $47,84. 5. What fraction is that, to the numerator of which, if I be added, it becomes, and if 1 be added to the denominator, it becomes? Ans.

6. The quick step of troops in marching, is 2 steps of 28 inches each in a second; how far will such troops travel in a day of eight hours?

7. The captain of a vessel, of which he owned, sold out the half of his share; he had before the sale $350 annual profit from it, besides his wages; how much remains to him annually after the sale of this part of his share?

8. A draper sold from a piece of cloth, t $5 the yard, one fifth at $4 per yard, and one sixth at $4,50 per yard; by this he obtained $168; how many yards were there in the piece?

Ans. 60.

9. On the first of January 1793, a royalist in Europe agreed with a democrat, to pay him 3 cents per day, until the restoration of the Bourbons, on condition of his paying him one louis d'or on $4,44, every day after that restoration. Taking the first of August, 1814, for the day of the return of the Bourbous, how would their account stand on the first of January, 1827, omitting all interest; and how, on calculating compound interest for every day from the epoch of these payments, to the first of January, 1827, at 5 per cent. annually?

Without interest, the first would have paid $236,43.

the second,

$21760,44.

10. A merchant gains in trade such a sum, that $320 has the same ratio to it, as five times the sum has to $2500; what did he gain? Ans. $400.

11. Two brothers comparing their ages, find that the sum of

both ages is to that of the elder, as 19 to 7, and to 30, as 9 to the age of the other; what are their ages?

Ans.

21. 9.

12. The difference of the sides of two square rooms is to the side of the greater, as 2 to 6, and the difference of their square content, is 128 feet; what are the sides of each of these rooms?

Ans.

18.

14.

13. The profits of two men in their work, are as 8 to 5, and the product of the numbers expressing their profits is 360; what was the profit of each? Ans. $15. $24.

14. A merchant gaining $7500 in 6 years, with a capital of $15000, what would he gain at the same rate in 11 years, with a capital of $21000?

15. It one man travels 52 miles in a day, walking 12 hours, and another 61 miles in 11 hours, what will be gained in time, on each, by sending both at the same time to meet from two places 180 miles from each other, to exchange dispatches, instead of sending them each the whole distance?

16. If 2100 bushels of oats last 200 horses, at a half bushel a day, twenty-one days, how long will 3700 bushels last 760 horses, at of a bushel per day?

17. What provision must be made for an army of 9560 men, in bread, if they shall receive 2 pounds per day, for 70 days, it being found by experience, that 5000 men will need in 25 days 3120 lbs. at 24 lbs. per day?

18. If 248 men in 5 days of 11 hours each, dig a trench 280 yards lon, 3 wide, and 2 deep, in how many days of 9 hours each, will 32 men dig a trench of 430 yard long, 6 yards wide and 3 deep? 19. A has given $15620, which laid in the common stock 6 y. 6 ms. B 66 46 7.921, (6

66 66 39567,

4266 7486

The capital is to be divided at the end of the time, and found to be double the amount put in by the stockholders; what is the share of each, in the whole amount?

20. Four merchants make a joint stock, under the following arrangements. A put in $15000, which remains 8 years and 6 months, during which time thesociation lasts; it is agreed, that as he is to take the chief direction, he shall have 2 per cent. previous to all profits, besides his share in the remaining profits. B puts in $20600 at the beginning Cputs in $13200 one year after the beginning; and as he is to work in the partnership, he is to have one and a half times the share of the profits which his capital would entitle him to, if he was not to work. D joins two and a half years after the beginning, with a capital of $60450; the partnership being dissolved, and the whole profits made, being $80560, what is the share of each ?

TABLES

of the Proportional Subdivisions, or Denominate Fractions, of Weights, Measures, Time, &c.

EXPLANATION. In the following tables, the denominations of the subdivisions will be found written in full, at the head of each table, and in their usual abbreviations within the tables themselves. The first number of each square, is the number of units of each subdivision required to make the unit of the kind found at the right hand; and the lower number in the same square, is the decimal fraction corresponding to the same subdivision and unit, carried to 7 decimals.