PROBLEMS, FOUNDED UPON THE FUNDAMENTAL RULES. 99. The following problems are founded upon the general principles of addition, subtraction, multiplication, and division, the fundamental operations of arithmetic, which have already been explained. 1. The parts of a number being given, to find the number. — Add the parts together (Art. 47). 2. The sum of two numbers and one of the numbers being given, to find the other number. — From the sum subtract the given number (Art. 50). 3. The difference between two numbers and the larger number being given, to find the smaller. — From the larger number subtract the difference (Art. 52). 4. The difference between two numbers and the smaller number being given, to find the larger. — Add the smaller number and the difference together (Art. 51). 5. The sum and the difference of two numbers being given, to find the numbers. — From the Slim subtract the difference and divide the remainder by 2, for the smaller number; add the difference to the smaller number, for the larger (Art. 52). Note. — In like manner, when the sum and differences are given, may be found any number of required numbers. After subtracting the differences from the sum, if there are 3 required numbers, divide by 3 for the smaller number; if 4, divide by 4, and so on. 6. The product of two numbers, and one of the numbers being given, to find the other numbers. — Divide the product by the given number (Art. 62). 7. The product of three numbers, and two of the numbers being given, to find the other number. — Divide the given product by the product of the two given numbers (Art. 72). 8. The dividend and quotient being given, to find the di-' visor. — Divide the dividend by the quotient (Art. 77). 9. The divisor and quotient being given, to find the dividend. — Multiply the divisor and quotient together (Art. 74). Examples. 1. A carpenter has contracted to build one house for 2763 dollars, another for 4650 dolfars, and a third for 8950 dollars. How much is he to receive for them all? Ans. 16363 dollars. 2. N. Chandler has invested in railroad stock and a small farm 929 dollars. If the amount invested in the stock was 279 dollars, how much did the farm cost him? Ans. 650 dollars. 3. Mount Black, the highest peak of the Blue Ridge, is 6476 feet high, which is 242 feet higher than Mount Washington, the highest peak of the White Mountains. What is the height of Mount Washington? 4. The city of Mexico, in 1519, was taken by Cortes, and, 328 years after, by General Scott. In what year did it yield to Scott? Ans. 1847. 5. Two travellers, A and B, meeting on a journey, found they had both travelled 1963 miles, and that A had travelled 199 miles more than B. What distance had each travelled? Ans. A, 1081 miles; B, 882 miles. 6. A father gave his three sons 4698 dollars, of which James received 250 dollars more than George, and Edwin 410 dollars more than George. What sum did each receive? Ans. George $1346; James $1596; Edwin $1756. 7. There was paid for 217 chests of tea 8463 dollars. How much was that a chest? 8. How many weeks will 684 bushels of oats last 19 horses, each horse consuming 3 bushels a week? 9. On dividing 3808 dollars among a certain number of men, it was found that the share of each was 224 dollars. Required the number of men. Ans. 17 men. 10. A certain missionary society divides its income among 99 missions, giving to each an average of 575 dollars. What is its income? Ans. 56925 dollars. 11. The product of 96, 22, and one other number is 63360. What is the other number? Ans. 30. 12. The divisor being 13 and the quotient 1101, what is the dividend? Ans. 14313. MISCELLANEOUS EXAMPLES. 1. What is the distance by railroad from Boston to Galena, it being from Boston to A1bany 200 miles, from A1bany to Niagara Falls 305, from Niagara Falls to Detroit 230, from Detroit to Chicago 282, from Chicago to Galena 171? 2. Sold J. Weimer my best horse for 175 dollars, my secondbest chaise for 87 dollars, and a good harness for 31 dollars, lie has paid me in cash 38 dollars, and has given me an order on S. Lantz for 12 dollars. How many dollars remain due? 3. Bought 97 barrels of molasses at $ 5 a barrel. Gave 17 barrels to support the poor, and the remainder was sold at $ 8 a barrel. Did I gain or lose, and how much? Ans. ,$ 155 gain. 4. It requires 1728 cubic inches to make one cubic foot; required the number of cubic inches in 3787 cubic feet. 5. If a garrison of 987 men are supplied with 175686 pounds of beef, how much will there be for each man? Ans. 178 1bs. 6. A1bert Peyton sold off from his farm 120 acres, gave his son 80 acres, and had remaining 160 acres; what number of acres did his farm contain before he disposed of any portion of it? Ans. 300 acres. 7. The annual revenue of a gentleman being $ 8395, how much per day is that equivalent to, there being 365 days in a year? Ans. $ 23. 8. What is the difference between half a dozen dozen, and six dozen dozen? Ans. 792. 9. Bought of F. Johnson 8 barrels of flour at $7 per barrel, and 3 hundred-weight of sugar at $ 8 per hundred. What was the amount of his bill? 10. George Adams bought an equal number of cows and oxen for 3952 dollars. For the cows he paid 31 dollars each, and for the oxen 45 dollars each. How many of each kind did he buy? Ans. 52. 11. If a certain quantity of provisions will sustain 13 men 4 days, how long would it sustain 1 man? Ans. 52 days. 12. The Globe Manufacturing Company has a capital of 250,000 dollars, divided into 500 shares. How much is each share? Ans. 500 dollars. 13. Purchased a farm of 500 acres for $ 17,876. I sold 127 acres of it at $ 47 an acre, 212 acres at $ 96 an acre, and the remainder at $ 37 an acre. What did I gain by my bargain? Ans. $14,402. 14. There is a certain island 18 miles in circuit, which A and B undertake to travel round, both starting from the same point and going round in the same direction. When A has traveled 17 miles and B 7 miles, how far apart are they? Ans. 8 miles. 15. If 15 men can reap a certain iield in 5 days, how long will it take 1 man to reap the same? Ans. 75 days. 16. What number is that, which being multiplied by 24, the product divided by 10, the quotient multiplied by 2, 32 subtracted from the product, the remainder divided by 4, and 8 subtracted from the quotient, the remainder shall be 2? Ans. 15. /34 X 6) (17 — 5). Ans. 125. 18. There are in the library of a certain school 683 books, which number will give 23 books to each pupil, and 16 books over; what is the number of pupils? 19. R. Howland in making a journey, after walking 12 miles and travelling 40 miles by stage, went by steamboat 5 times the distance he had travelled by stage, and by cars 6 times as far as he had walked, and 7 miles besides. What was the length of his journey? Ans. 331 miles. 20. At an election A and B were candidates for the same office, and the whole number of votes cast lor them was 9891, of which B received 1211 majority. What number of voles did each receive? Ans. A, 4340; B, 5551. 21. The product of 3 numbers is 4080; one of the numbers is 15, and another 16. What is the third number? 22. How many tons of coal at 6 dollars a ton will be required to pay for 17 yards of cloth at 4 dollars a yard and 32 bushels of wheat at 2 dollars a bushel? Ans. 22 tons. 23. James Cooper has manufactured in 4 years 5608 pairs of shoes, making each successive year 100 pairs more than the year before; how many pairs did he manufacture each year? Ans. 1252; 1352; 1452; 1552. 24. How many years will it take a young man earning 45 dollars, and spending 35 dollars of it, every month, if he have already 620 dollars, to lay up enough more to pay for a house costing 1100 dollars? Ans. 4 years. 25. If the product of the divisor by the quotient be 19782, and the remainder 31, what is the dividend? Ans. 19813. 26. John Franklin purchased railroad stock to the amount of 4473 dollars, and sold a part of it for 1885 dollars, obtaining 65 dollars a share, which was at a loss of 6 dollars on every share sold; but the stock advancing much in value, he was able to dispose of the balance so as to gain by the whole operation 812 dollars. What did he get a share for the balance of the stock? Ans. 100 dollars. UNITED STATES MONEY. Art. 100i United States Monet is the legal currency of the United States. It was established by Congress in 1786. Its denominations and their relative values are shown in the following TABLE. In accounts and ordinary business transactions, the only denominations mentioned are dollars and cents, eagles being expressed as dollars, dimes as cents, and mills as a fraction of a cent. The dollar is the integer, or unit of measure of United States money; and therefore dimes are tenths of a dollar; cents, hundredths; and mills, thousandths. |