18. Sold 120 pieces of cloth at $45 a piece, and gained thereby $1026; how much did it cost by the piece? Ans. $37.20. 19. A flour merchant paid $3088.25 for some flour. He sold 425 barrels at $6 a barrel, and the remainder stood him in $4.50 a barrel; how many barrels did he purchase? Ans. 521.

20. If 36 engineers receive $6315.12 for one month's work, how many engineers will $21927.50 pay for one month at the same rate? Ans. 125.

21. A person having $1378.56, wishes to purchase a house worth $2538, and still have $750 left with which to purchase furniture; how much more money must he have? Ans. $1909.44.

22. A mechanic earns on an average $1.87 a day, and works 22 days per month. If his necessary expenses are $25 a month, how many years will it take him to save $1116, there being 12 months in a year? Ans. 6 years.

23. Bought 27.5 barrels of sugar for $153.75, and sold it at a profit of $3.62 a barrel; at what price per barrel was it sold? 24. A man expended $70.15 in the purchase of rye at $.95 a bushel, wheat at $1.37 a bushel, and corn at $.73 a bushel, buying the same quantity of each kind; how many bushels in all did he purchase? Ans 69 bushels.

25. A farmer bought a piece of land containing 375 acres, at $22 per acre, and sold of it at a profit of $1032; at what price per acre was the land sold? Ans. $27.75.

26 If 3 cords of wood cost $11.37%, how much will 20 cords cost? Ans. $65.40§. 27. If of a hundred pounds of sugar cost $6%, how much can be bought for $16.75, at the same rate?

Ans. 5.5 hundred pounds. 28. A man sold a wagon for $62.50, and received in payment 12 yards of broadcloth at $3 per yard, and the balance in coffee at 12 cents per pound; how many pounds of coffee did he receive? Ans. 175 pounds.

29. Bought 320 bushels of barley at the rate of 16 bushels for $10.04, and sold it at the rate of 20 bushels for $173; how much was my profit on the transaction? Ans. $79.20.

PROBLEMS

INVOLVING THE RELATION OF PRICE, COST, AND QUANTITY.

PROBLEM I.

253. Given, the price and the quantity, to find the cost. ANALYSIS. The cost of 3 units must be 3 times the price of 1 unit; of 8 units, 8 times the price of 1 unit; of of a unit, times the price of 1 unit, etc. Hence,

RULE. Multiply the price of ONE by the quantity.

PROBLEM II.

254. Given, the cost and the quantity, to find the price. ANALYSIS. By Problem I, the cost is the product of the price multiplied by the quantity. Now, having the cost, which is a product, and the quantity, which is one of two factors, we have the product and one of two factors given, to find the other factor. Hence, RULE. Divide the cost by the quantity.

PROBLEM III.

255. Given, the price and the cost, to find the quantity. ANALYSIS. Reasoning as in Problem II, we find that the coɛt is the product of two factors, and the price is one of the factors, Hence, RULE. Divide the cost by the price.

PROBLEM IV.

256. Given, the quantity, and the price of 100 or 1000, to find the cost.

ANALYSIS. If the price of 100 units be multiplied by the number of units in a given quantity, the product will be 100 times the required result, because the multiplier used is 100 times the true multiplier. For a similar reason, if the price of 1000 units be multiplied by the number of units in a given quantity, the product will be 1000 times the required result. These errors can be corrected in two ways,

1st. By dividing the product by 100 or 1000, as the case may be; or, 2d. By reducing the given quantity to hundreds and decimals of a hundred, or to thousands and decimals of a thousand. Hence,

RULE. Multiply the price by the quantity reduced to hundreds and decimals of a hundred, or to thousands and decimals of a thousand.

NOTE. In business transactions the Roman numerals C and M are commonly used to indicate hundreds and thousands, where the price is by the 100 or 1000.

PROBLEM V.

257. To find the cost of articles sold by the ton of

2000 pounds.

ANALYSIS. If the price of 1 ton or 2000 pounds be divided by 2, the quotient will be the price of ton or 1000 pounds. We then have the quantity and the price of 1000 to find the cost. Hence,

RULE. Divide the price of 1 ton by 2, and multiply the tient by the number of pounds expressed as thousandths.

EXAMPLES IN THE PRECEDING PROBLEMS.

1. What cost 187 barrels of salt, at $1.32 a barrel?

quo

Ans. $246.84.

2. What cost 5 firkins of butter, each containing 70 pounds, Ans. $66.09.

at $3 a pound?

3. If the board of a family be $501.87 for 1 year, how much is it per day? Ans. $1.37.

4. At $.10 a dozen, how many dozen of eggs can be bought for $18.48?

Ans. 176.

5. What is the value of 140 sacks of guano, each sack containing 162 pounds, at $17 a ton? Ans. $201.9061. 6. What will be the cost or 3240 peach trees at $161⁄2 per hundred? Ans. $534.60.

7. At $66.44 a ton, what will be the cost of 8423 tons of railroad iron? Ans. $55992.31. 8. A gentleman purchased a farm of 325.5 acres for $10660; Ans. $32.75.

how much did it cost per acre?

9. What will be the cost of 840 feet of plank at $1.94 per C;

and 1262 pickets at $12 per M?

Ans. $32.071. 10. At $1 a bushel, how many bushels of wheat can be bought Ans. 25 bushels.

for $37.683?

11. What will be the cost of 2172 pounds of plaster, at $3.875 a ton? Ans. $4.2081.

12. What cost ğ of 456 bushels of potatoes at $.371⁄2 a bushel? 13. If 32 barrels of apples cost $81.25, what is the price per barrel? Ans. $2.50. 14. What must be paid for 24240 feet of timber worth $9.37} per M.? Ans. $227. 15. At $5§ an acre, how many acres of land can be bought for $4234.37? Ans. 7527. 16. How much must be paid for 972 feet of boards at $20.25 per M, 1575 feet of scantling at $2.87 per C, and 8756 feet of lath at $7 per M? Ans. $130.634.

17. What is the value of 1046 pounds of beef at $4§ per hundred pounds? Ans. $48.37.

18. What is the value of 5840 pounds of anthracite coai at $4.7 a ton, and 4376 pounds of shamokin coal at $5.25 a ton? 19. At $2.50 a yard, how much cloth can be purchased for $2? 20. What is the value of 3700 cedar rails at $5 per C? 21. How much is the freight on 3840 pounds from New York to Baltimore, at $.96 per 100 pounds? Ans. $36.864.

22. What is the value of 9 pieces of broadcloth, each piece containing 27 yards, worth $27 a yard? Ans. $715.871. 23. At $.42 a pound, how many pounds of wool may be bought for $80.745? Ans. 1924.

24. What will be the cost of 327 feet of boards at $15 per M; 672 feet of siding at $1.62 per C, and 1108 bricks at $41 per M? Ans. $20.693. 25 At $3 per yard, how many yards of silk may be bought for $15? Ans. 18. 26. How much must be paid for the transportation of 18962 pounds of pork from Cincinnati to New York, at $10 a ton?

27. If 15 yards of silk cost $27.9, what is the price per yard? 28. What cost 27860 railroad ties at $125.38 per thousand? 29. If .7 of a ton of hay cost $131, what is the price of 1 ton? 30. What is the value of 720 pounds of hay at $12.75 a ton, and 912 pounds of mill feed at $15 a ton? Ans. $11.658.

LEDGER ACCOUNTS.

258. A Ledger is the principal book of accounts kept by merchants and accountants. Into it are brought in summary form the accounts from the journal or day-book. The items often form long columns, and accountants in adding sometimes add more than one column at a single operation, (68).

259. A Debtor, in business transactions, is a purchaser, or a person who receives money, goods, or services from another; and 260. A Creditor is a seller, or a person who parts with money, goods, or services to another.