S 6. Suppose a man should raise on the several fields of has farm the following quantities of grain, viz: 685 bushels, 97 bushels, 330 bushels, and 1000 bushels,-how many bushels would he raise altogether? Ans. 2112 bushels. 7. Allowing a person's estate to be estimated as follows, viz: real estate 9000 dollars, personal property 1375 dollars, recoverable debts 875 dollars, and cash 300 dollars,-what would be the value of his estate? Ans. 11550 dollars. 8. Admitting I bought of A 500 bushels of wheat, of B 934 bushels, of C 83 bushels, and of D 125 bushels,-how many bushels did I buy in all? Ans. 1642 bushels. 9. Three persons deposite flour in the same warehouse; the first, 43 barrels; the second 150 barrels; and the third, 89 barrels. What quantity do they all deposite? Ans. 282 barrels. 10. A merchant bought four pieces of cloth; the first for 225 dollars, the second for 310 dollars, the third for 279 dollars, and the fourth for 95 dollars. What did the whole cost him? Ans. 909 dollars. 11. If a merchant buy a stock of goods for 5000 dollars, for what sum must he sell the goods so as to gain by them 475 dollars? Ans. 5475 dollars. For 12. Bought a barrel of sugar for 15 dollars, a barrel of molasses for 13 dollars, and a sack of coffee for 20 dollars. what sum must the whole be sold to gain 10 dollars ? Ans. 58 dollars. 13. A person on a journey travels, the first week 255 miles; the second, 240 miles; the third and fourth, each 200 miles. How far did he travel in the four weeks? Ans. 895 miles. 14. Four persons, A, B, C, and D, engage in speculation. A gains 75 dollars, B 100 dollars, and C and D each 235 dollars; what sum was gained by all together? Ans. 645 dollars. 15. A farmer bought three plantations for 3750 dollars each, and sold them again so as to make 1000 dollars on the whole. For what sum did he sell the three. Ans. 12250 dollars. 16. A draper sold four bales of linen; the first and second contained each 480 yards; the third and fourth each 542 yards. How many yards did he sell? Ans. 2044 yards. 17. Bought of A 325 bushels of wheat; of B, 280 bushels; of C as much as from A; and of D as much as from B. What quantity of wheat did I buy in all ? Ans. 1210 bushels. 18. A merchant bought at one time 375 barrels of flour, for 1875 dollars; and at another 400 barrels for 2000 dollars. What quantity of flour did the merchant buy, and for what sum ? Ans. 775 barrels, for 3875 dollars. 19. Find the Sum 345+-480-+2346+7864. Ans. 11035. Ans. 5552. Ans. 6424. Ans. 61127. Ans. 1125. 28. A lends to B 2500 dollars; to C 3000; and has 5325 dollars left. What sum had A at first? Ans. 10825 dollars. 29. A speculator bought stock at one time for 325 dollars; and at another time for 705 dollars. In selling the whole, he realized a gain of 175 dollars; for what sum did he sell? Ans. 1205 dollars. 30. A gentleman is 15 years older than his wife, and she is 20 years older than their eldest son, who is 29 years of age. Required the gentleman's age, and the age of his wife? Ans. His age is 64 years; hers 49. 31. A, B, and C form a partnership in trade. A puts in 4250 dollars; B, 2000 dollars; and C as much as A and B together; what is their whole stock in trade? Ans. 12500 dollars. 32. Bought at one time 75 yards of cotton, and 100 yards of linsey; at another, 37 yards of cotton, and 87 yards of linsey; and at another, 125 yards of cotton, and 9 yards of linsey. What quantity of each kind did I buy? Ans. 237 yards of cotton, and 196 of linsey. 33. A merchant bought cloth for 375 dollars, and silk for 95 dollars. In selling, he gained 50 dollars on the cloth, and 45 dollars on the silk; for what sum did he sell the whole ? Ans. 565 dollars. 34. A grocer paid 300 dollars for sugar, 174 dollars for coffee, 85 dollars for rice, and 56 dollars for tobacco. He sold the sugar at a profit of 25 dollars, and the other articles at cost; what did he get for the whole ? Ans. 640 dollars. 35. A father bequeaths to his only daughter 2500 dollars, and to each of his two sons, 500 dollars more than to his daughWhat sum did each son receive, and what was the amount of the several bequests? Each son, 3000 dollars, ter. Ans. Amount, 8500 dollars. 36. Several persons contributed towards the establishment of a library. A gave 200 dollars, and B 50 dollars more than A; C gave 300 dollars, and D 25 dollars more than C. was the whole amount contributed? What Ans. 1075 dollars 37 The produce of two farms was as follows, viz: of the first, 785 bushels of wheat, and 250 of rye; of the second, 1000 bushels of wheat, and 113 of rye. What was the entire produce of the farms (§ 26)? Ans. 1785 bushels of wheat, and 363 of rye. 38. A merchant bought 4 bales of cotton; the first and second contained 470 yards each; and the third and fourth, 532 yards each. What was the number of yards purchased? Ans. 2004 yards. 39. Bought live stock as follows, viz: of A 13 cows, 16 oxen, and 120 sheep; of B 24 cows, 30 oxen, and 153 sheep: and of C 100 cows, and 425 sheep. It is required to find the amount of stock purchased (§ 26). Ans. 137 cows; 46 oxen; 698 sheep. 40. A has 2375 dollars; B 150 dollars more than A; and C as much as A and B together. What sum is possessed by C, and what by the three together? SC has 4900 dollars. The three 9800 dollars. Ans. 41. A farmer has in store at one place 500 bushels of wheat, 325 of oats, and 50 of corn; and at another, 475 bushels of wheat, 75 of oats, and 83 of corn. What amount of produce has the farmer in store? Ans. 975 bushels of wheat; 400 of oats; 133 of corn. 42. Bought a quantity of cloth for 386 dollars, of cotton for 200 dollars, and of silk for 150 dollars. The cloth was sold at a profit of 73 dollars, the cotton at a profit of 35 dollars, and the silk at cost. What was the whole sold for? Ans. 844 dollars. 43. The population of each of the grand divisions of the Earth, is estimated as follows, viz: of Europe, at 238 millions, 473 thousand, nine hundred and fifty-seven; of Asia, at 390 millions; of Africa, at 65 millions; of North America, at 35 millions; of South America, at 15 millions, 240 thousand; and of Oceanica, at 20 millions. What then is the whole population of the several grand divisions of the Earth? Ans. 763713957 inhabitants. SUBTRACTION. § 29. SUBTRACTION consists in finding the difference between two numbers; that is, the remainder when the less number is taken from the greater. The less number is called the subtrahend, and the greater the minuend. Thus 4 from 9 leaves 5; then 4 is the subtrahend, 9 the minuend, and 5 the difference or remainder. What is the difference between 5 and 8? Between 6 and 10? Between 9 and 15? Between 8 and 17? Between 10 and 19? Addition and Subtraction. § 30. Addition and Subtraction are the reverse of each other. In Addition, the parts are given, to find the sum or whole; in Subtraction, the sum or whole, and one of its parts, are given, to find the other part. The sum being 10, and one of its parts 7, what is the other part? The sum being 13, and one part 6, what is the other part? The sum being 19, and one part 12, what is the other part? $ 31. The sign Sign of Subtraction. called minus, placed between two numbers, signifies that the one before which it stands, is to be subtracted from the other. Thus 9-4, 9 minus 4, signifies 4 subtracted from 9. How many is 8-5? How many is 10-3? 13-7! 15-4? 18-11? 20-10? 14-9? 17-8? 21-10? 25-15? Difference of Concrete Numbers. $ 32. The difference of two similar concrete numbers, is a concrete number of the same kind. Thus the difference of 5 cents and 8 cents is 3 cents. What is the difference between 12 pounds and 3 pounds? Between 18 days and 9 days? Between 20 dollars and 12 dollars? $33. Two dissimilar concrete numbers cannot be subtracted, the one from the other. Thus we cannot subtract 5 pounds from 8 days. Constant Difference. § 34. The Difference of two numbers remains the same, when those numbers are equally increased or diminished. What is the difference between 4 and 7? Between 4+1 and 7+1 ? Between 5 and 9? Between 5+2 and 9+2? Between 7 and 12? Between 7+10 and 12+10? Between 20-9 and 15-9? RULE IV. $ 35. To Subtract one Number from another. 1. Set the less number under the greater, with units under units, tens under tens, &c. 2. Proceeding from right to left, take each lower figure from the one above it, and underneath set the remainder. 3. If the lower figure exceed the upper, add 10 to the upper figure; from the sum subtract the lower, and then add 1 to the next lower figure before subtracting it. EXAMPLE. To find the Difference between 654739 and 80657. 654739 574082 Having set the less number under the greater, with units under units, tens under tens, &c., and drawn a line below them, We begin at the right, and say 7 from 9 leaves two; the 5 being greater than the 3 above it, we say 10 and 3 are 13, and 5 from 13 leaves 8; then adding 1 to the 6, making 7, we say 7 from 7 leaves 0; 0 from 4 leaves 4; 10 and 5 are 15, and 8 from 15 leaves 7; there being no figure under the 6, the 1 to be added there makes 1 for that place, then 1 from 6 leaves 5. The Difference required is 574082. The 10 added to any upper figure is always equal to the 1 added to the next lower figure (§ 11); so that these additions preserve the same difference between the two given numbers (§ 34). In the preceding example, the 10 tens added to the 3 tens, are equal to the 1 hundred added to the 6 hundreds; in like manner the 10 added to the 5 in the upper number is equal to the 1 added to the lower nunber, and subtracted from the 6. The several figures in the remainder express the differences between the corresponding units, in their several orders, in the two given numbers or those numbers equally increased in the process of subtracting. |