$3 a head more than B; how much did each get for his cattle? Ans. A got $596.921; B $483.07.

Ans..

12. What number is it to which of of be added, the sum will be 1? 13. What number is it whose, and added together make 78? Ans. 72.

14. To find a number, which being multiplied by 3, subtracting 5 from the product and the remainder divided by 2, if the number sought be added to the quotient, the sum will be 40? Ans. 17.

and

15. What number is it which being added to 4, also multiplied by 4, the product shall be treble the sum? Ans. 12.

16. To find a number, to which if 11 be added and 7 subtracted from the same number, the sum of the addition will be double the remainder? Ans. 25.

17. To find a number which being added to itself and the sum being multiplied by the same, and the same number still subtracted from the product; and lastly, the remainder divided by the same, the quotient may be 13?

Ans. 7.

18. To find three numbers such, that the sum of the first and second shall be 15, the sum of the first and third 16, and the sum of the second and third 17?

Ans. 7, 8 and 9.

19. Three persons, A, B and C, owe certain sums of money, so that A and B owe $210, B and C 290, and C and A 400; what did each of them owe?

Ans. A 160, B 50, and C 240. 20. A man having a certain number of dollars in his hand, being asked how many he had, replied if the number be divided by 5 and 19 added to the quotient, I shall then have $23; how many dollars had he? Ans. 20. 21. A person said he had 20 children, and that it happened there was a year and a half between each of their ages, his eldest was born when he was 24 years old, and

the age

age?

of the youngest is now 21; what was the fathers' Ans. 73 years.

22. When I sold cloth at $7 per yard, I gained 561 cents; what would I gain by selling 3 pieces, which cost me $400? Ans. $32.144.

23. A and B dissolve partnership, and equally divide their gain; A's share which was $332.50 lay for 21 months; B's for 9 months only; the adventure of B is required? Ans. $775.831.

24. I bought 25 yards of lace at 30 cents for the first yard, and for the last yard 96; the price of each yard increasing in arithmetical progression; what did the whole amount to? Ans. $15.75.

25. A case of dry goods amounting to £230 5s. sterling is sold in Philadelphia, at 20 per cent. advance; what is the amount in American currency? Ans. $1228.

26. What is the difference between the interest of $1000 at 6 per cent. for 8 years, and the discount of the same sum at the same rate, and for the same time?

Ans. the interest exceeds the discount by $155.671. 27. A gentleman sells a piece of cloth at $56.25, and thereby loses 7 per cent,; what was the first cost? Ans. $60.47.

28. A has 28 cwt. of cotton which cost him $264; how must he rate it per lb., to D, so that by taking his note payable at 9 months he may clear $30, allowing interest at 6 per annum? Ans. 9 c.

cent. per

29. In a series of proportional numbers the first is 5, the second is 8, the product of the second and third is 78.4, what is the difference of the first and fourth?

Ans. 10.68.

30. If 3481 soldiers are to be placed in square file,

how many are to be set in each rank?

Ans. 59.

31. A can do a piece of work in 10 days, B in 13, set them both at it, in what time will it be finished?

Ans. 5.

32. A stationer sold quills at $10 per thousand, by which he gained of the money, but growing scarce raised them to $12,50 per thousand, what is the gain per cent. by the latter price? Ans. 100 per ct.

33. Richard Cotter, of Baltimore, remits to William Denman, of New York, a bill of exchange on London, the avails of which he wishes to be invested in goods on his account. Denman disposes of the bill at 7 per cent. advance, and received $9675.00, having reserved for himself per cent. on the sale of the bill, and 2 per cent. for commission, what will remain for investment, and how much was the bill drawn for?

Ans. for investment $9457.314. The bill was drawn for £2025 sterling.

SOUND.

Sound if not interrupted, will move at the rate of about 1150 feet in a second of time.

34. I have seen the flash of a cannon fired from Fort. McHenry, and heard the report 47 seconds afterwards, what distance was the fort from where I stood?

Ans. 54050 feet.

35. Bought a quantity of cloth for $750,

of which I found to be inferior, which I had to sell at $1.25 per yard, and by this I lost $100, what must I sell the rest at per yard, that I shall lose nothing by the whole?

Ans. $3.15. 36. A circular fish pond is to be dug in a garden that shall take up just half an acre, what must be the radius of the circle? Ans. 27.75 yds.

37. Bought a horse which was worth 30 per cent. more than I gave for him, but having been injured I sold him for 25 per cent. less than what he cost, and thereby lost $55 on his real value, what was received for the horse? Ans. $75.

38. A son having asked his father's age the father thus replied: "your age is 8 years, to which if five-eights of

both our ages be added, the sum will be my age," what Ans. 34 years, 8 months.

was the father's age?

39. A merchant sold goods to a certain amount on a commission of 4 per cent., and having remitted the net proceeds to his correspondent, he received per cent. for prompt payment, which amounted to $15.60, what was the amount of his commission? Ans. $260.00.

40. How many thousand brick would be required to build the walls of a house 40 feet long, 30 feet wide, and 20 feet high, admitting the walls to be a foot thick, and that each brick was 8 inches long, 4 inches wide, and 2 inches thick? Ans. 73440.

41. Purchased merchandise to the amount of $2000, viz: $400 at 3 months, $800 at 6 months, and $800 at 9 months. Required the average time of payment.

Ans. 6 months.

42. Bought several parcels of goods at different times and on various credits.

1841.

May 11, a bill am'ting to $75 at 1 mo. crd. due June 10.

Required the average time of payment?

Ans. July 14th, at 9 o'clock in the morning.

43. The ball on the top of St. Paul's Church is 6 feet in diameter, what did the gilding of it cost at 3d. per square inch? Ans. £237 10s. 1d. 44. There is a conical glass, 6 inches high, 5 inches wide at the top, and is part filled with water, what must be the diameter of a ball, let fall into the water, that shall be immersed by it? Ans. 2.445+ in.

45. How much larger is a cube, that will contain a globe of 20 inches in diameter, than a cube inscribed within such globe? Ans. lar. 8000 in. smaller 1539 in.