A Written Arithmetic, for Common and High Schools

55. If a body in falling descends 16 feet in the first second of time, three times 16 in the next second, and five times 16 feet in the third second, how far will it fall in three seconds?

56. Owing a man in Paris 1325 francs, I have shipped to him $375 worth of rice. If the franc is worth 183 cents, how much have I overpaid him in Federal money

57. 72 oz. of gold are to be divided among 3 men and a boy,— the boy to have half as much as a man; what will each have? 58. If the wages of a man per month are $354, and if the wages of 3 boys are equal to the wages of 2 men, what will be the wages of 10 men and 30 boys for a month?

59. What is that number to which if of itself be added the sum will equal 64?

Ans. 40. 60* If from 5 times a certain number 19 is subtracted, and the remainder is 1874, what is the number?

61. I sold my watch for $72, which was more than I gave for it; what did it cost me?

62. Bought a horse and saddle for $75, giving as much for the saddle as for the horse; what was the cost of each?

63. A boy, being asked the age of his dog, replied, “If of his be added to his age, the sum will be 13 years." What was his age?

age

64. Being asked the age of his father, he said, were added to of his age, the sum would equal What was his age?

65. Being asked his own age, he answered, "If added to of my age, the sum would equal What was his age! ?

“If 12 years

of his age." Ans. 48 years.

2 years were of my age." Ans. 16 years.

66. A can build a wall in 3 days, and B can do the same work in 4 days. What part of the work can each do in one day! What part can both do in one day? In how many days car both do it working together?

67. C can do a piece of work in 5 days, and What time will be required for both to do it?

Ans. 14 days. D in 8 days.

Ans. 3 day

68* If E can do the same work in 7 days, how long would be required for C, D, and E, to do it working together? Ans. 21 days.

69* If A, B, and C can do a piece of work in 6 days, and A and B can do the same work in 8 days, in what time can C do it alone? Ans. 24 days. 70** Shipped to Havre 2000 bbls. of flour, which I sold at $73 per bbl.; received in return 500 hhds. of wine, worth $211 per hhd.; what sum is still due me?

cargo of teas, the whole cargo

71* A merchant owned & of a worth $65000; he sells of his share for $8583.33; does he gain or lose, and how much?

72. From a tank containing 184 gallons of water, 20 gallons were drawn out; if g of what then remained was equal to of what afterwards rained in, how much rained in? How much Idid the tank then contain? Ans. 236 gallons.

73* I pay $700 for a piece of land; cut 52 cords of wood from it, which I sell at $5.40 a cord; I pay $1g a cord for cutting and hauling the wood, and $10 for surveying the land; I divide 3 acres of it into house lots of acre each; 4 of these I sell at $175 each, and the rest at $162.50 per lot. Reserving 2 acres for myself, valued at $300, I sell the remainder of the land for $600, what do I gain? Ans. $2388.18.

74 Messrs. B, D, W, and S, built a drain together, each agreeing to pay his proportion of whatever he occupied. B occupied 20 feet alone, B and D 22 feet, B, D, and W, 140 feet. B, D, W, and S, 18 feet. The drain was built at a cost of 331 cents per foot; what was each person's share of the cost? NOTE. -B's share=20 × 331+ 22x33140X33+ 18x331

Ans. B, $27.38%; D, $20.72%; W, $17.05; S, $1.50. 75* A, B, C, and D, hired a team together in Boston for a journey north, each agreeing to share the expense for the distance he rode. At Reading, 14 miles from Boston, A got out; at Andover, 8 miles further, B got out; at Lawrence, 4 miles further, C left, and D went on alone 8 miles to Haverhill. Re

turning, he took up C, B, and A, where he left them, and all rode into Boston. They paid $8.50 for the use of the team; what was each one's share?

NOTE.-The distance from Boston to Haverhill is 34 miles; the price for I mile out and back is $8.50$.25; D's share is 1425+ 8×25 + 4x25 +8 x 25.

Ans. A, $.87; B, $1.54; C, $2.04f; D, $4.04f.

149. GENERAL REVIEW, No. 3.

1. What are the prime factors of 420?

2. Divide 15 X 7 × 12 × 8, by 21 × 10 × 3 × 4.

3. What is the greatest common divisor of 21, 84, and 51? 4. What is the least common multiple of 42, 9, 14, and 12? 5. Reduce and to their lowest terms.

6. Reduce 254 to an improper fraction.

7. Reduce £88 to a mixed number.

8. Reduce of of 2 of 65 to a simple fraction.

9. Reduce,, and, to a common denominator.

10. Reduce 18, 14, and 8%, to the least common denominator. 11. Add 2 of 4, 14, and 94.

17. Change, and to simple fractions.

18. What part of 83 is 21?

19* What is the greatest common divisor of,, and 2}! 20 What is the least common multiple of,, and ? 21. How many fourths of of 40 in 34 × ÷ of 39?

For changes, see Key.

COMPOUND DENOMINATE NUMBERS.

150. Numbers are either Simple or Compound. 151. A Simple Number is a number expressed in units of one denomination; as, 5 books, 7 pens.

152. A Compound Number is a number expressed in units of two or more denominations, but of the same nature; as, 5 pounds 6 ounces of sugar, 3 years 2 months 4 days of time. 153. Reduction is the process of changing the denomination of numbers without altering their value.

154. Reduction Descending is the process of changing numbers to numbers of equal value in lower denominations; thus, 1 dollar 100 cents.

155. Reduction Ascending is the process of changing numbers to numbers of equal value in higher denominations; thus, 100 cents 1 dollar.

156. Compound numbers express Currency, Weight, and Measure.

CURRENCY.

Every nation has its own currency.

That of the United

States has already been given (Art. 68), but the table will be inserted here for the sake of uniformity.

157. FEDERAL MONEY.

The denominations are eagles, dollars, dimes, cents, and mills, The legal coins in circulation are as follows:

Three Cent piece

.03.

Copper and nickel Cent, and Two Cent pieces.

copper and silver

NOTE. The gold coin is hardened by an alloy of (the silver not to exceed the copper). The silver coin is hardened by copper. The cent coined since 1856 has 88 parts of copper to 12 of nickel. The two-cent piece, coined 1864, has 95 parts copper to 5 of tin and zinc. TABLE.

NOTE.-Mill is derived from the Latin mille, one thousand, because 1000 mills 1 dollar, the unit of computation; cent from Latin centum, one hundred, because 100 cents 1 dollar; dime from the French dime, a tenth, as a dime is one tenth of a dollar; dollar from the German thaler, dollar, dollars having been first coined in Germany.

EXERCISES.

1. Write 3 E. $2. 7 d. 5 c. 2 m. as it is usually written.

2. Write 162 E. $8. 3 d. 9 c. 8 m. as it is usually written.

Ans. $32.752.