7. To find the cost when the price of one is $7.50. RULE.—Annex a cipher ta the quantity, consider as dollars, and subtract 1. 8. To find the cost when the price of one is 04. RULE.- Point off one place in the quantity, consider as dollars, and subtract 1. 9. To find the cost when the price of one is 1314. RULE.—Point off one place in the quantity, consider as dollars, and add t. 10. To find the cost when the price of one is $1.331. RULE.—Add } to the quantity, and consider as dollars. 11. To find the cost when the price of one is $1.10. RULE. -Add to to the quantity, and consider as dollars. 12. To find the cost when the price of one is $1.20. RULE.—Add to the quantity, and consider as dollars. 13. To find the cost when the price of one is $1.35. RULE.—Add 1 and to to the quantity, and consider as dollars. 14. To find the cost when the price of one is $1.75. RULE.- Add 1 and 1 to the quantity, and consider as dollars. 15. To find the cost when the price of one is $3.333. RULE. - Annex a cipher to the quantity, consider as dollars, and divide by 3. INSTRUCTIONS FOR FINDING QUANTITY. 300. 1. To find the quantity of articles that any given sum of money will purchase, when the price of one is 50¢. RULE. — Multiply the dollars, considered as quantity, by 2. 2. To find the quantity when the price of one is 3314. RULE.—Multiply the dollars, considered as quantity, by 3. 3. To find the quantity when the price of one is 25%. RULE.—Multiply the dollars, considered as quantity, by 4. 4. To find the quantity when the price of one is 204. RULE.—Multiply the dollars, considered as quantity, by 5. 5. To find the quantity when the price of one is 1634. RULE.—Multiply the dollars, considered as quantity, by 6. 6. To find the quantity when the price of one is 1214. RULE.—Multiply the dollars, considered as quantity, by 8. 7. To find the quantity when the price of one is 10%. RULE.—Annex a cipher to the dollars, and consider as quantity. 8. To find the quantity when the price of one is 814. RULE.—Multiply the dollars, considered as quantity, by 12. 9. To find the quantity when the price of one is 644. RULE.—Multiply the dollars, considered as quantity, by 16 10. To find the quantity when the price of one is 5%. RULE. —Annex a cipher to the dollars, consider as quantity, and multiply by 2. 11. To find the quantity when the price of one is 31¢. RULE. —Annex a cipher to the dollars, consider as quantity, and multiply by 3. 12. To find the quantity when the price of one is 214. RULE.—Annex a cipher to the dollars, consider as quantity, and multiply by 4. 13. To find the quantity when the price of one is 134. RULE.-Annex a cipher to the dollars, consider as quantity, and multiply by 6. 14. To find the quantity when the price of one is 174. RULE.-Annex a cipher to the dollars, consider as quantity, and multiply by 8. MISCELLANEOUS CONTRACTIONS. 301. 1. To find the quantity when the price of one is $1.25. RULE. — Point off one place in the dollars, consider as quantity, and multiply by 8. 2. To find the quantity when the price of one is $1.663. RULE.—Point off one place in the dollars, consider as quantity, and multiply by 6. 3. To find the quantity when the price of one is $2.50. RULE.—Point off one place in the dollars, consider as quantity, and multipty by 4. 4. To find the quantity when the price of one is $6.66ş. RULE. - Point off one place in the dollars, consider as quantity, and add 1. 5. To find the quantity when the price of one is $7.50. RULE.-Point off one place in the dollars, consider as quantity, and add t. 6. To find the quantity when the price of one is $12.50. RULE.—Point off two places in the dollars, consider as quantity, and multiply by 8. MISCELLANEOUS EXAMPLES IN FINDING QUANTITY. 302. EXAMPLE 1.—How many pounds of tea, worth 663¢ per lb., can be bought for $147 ? EXPLANATION.—Since the price of one pound is contained 17 times in $1, the number of pounds bought will be 14 times the number of dollars invested ; hence, add to the number of dollars (as pounds) t of itself, and the result will be the number of pounds purchased. EXAMPLE 2.—How many pounds of tea, at 75$ per lb., will $419.25 purchase ? EXPLANATION.-Since the price of one pound is contained 1j times in $1, the number of pounds bought will be 11 times the number of dollars invested ; hence, add to the number of dollars of itself, and the result will represent the number of pounds 'purchased. EXAMPLE 3.—How many pounds of tea, at 873per lb., can be bought for $316 ? EXPLANATION. —Since the cost of one pound is contained 11 times in $1, the number of pounds purchased will be greater than the dollars invested. EXAMPLE 4.—At 8334 per yard, how many yards of cloth can be bought for $1128.50 ? EXPLANATION.-Since the price of one yard is contained 13 times in $1, we can buy } more yards than we have dollars to invest. EXAMPLE 5.–At 80$ per yard, how many yards can be bought for $246.25 ? EXPLANATION.-Since $1 will buy 11 yards, $246.25 will buy 246.25 times 11 yards; hence, to the number of dollars add 1 of itself. REMARK. — The teacher can profitably extend these exercises for mental and written drili for pupils. MISCELLANEOUS EXAMPLES IN FINDING QUANTITY. 93 303. To Find the Cost when the Price is an Aliquot Part of a Dollar. EXAMPLE.- Required, the cost of 546 gallons of molasses, at 3314 per gallon ? EXPLANATION.-Since 33}¢ is 1 of $1, 3 gallons would cost $1 ; and if $1 will buy 3 gallons, it will require as many dollars to buy 546 gallons as 3 is contained times in 546, or $182. Rule.- Divide the quantity, considered as dollars, by the number of units of the quantity that will cost $1. EXAMPLES FOR PRACTICE. 304. Find the cost of 1. 286 lb. of tea, at 50¢ per lb. 7. 1238 cans of salmon, at 20° per can. 2. 1152 yd. of linen, at 331$ per yd. 8. 756% gal. of cider, at 814 per gal. 3. 527 lb. of lard, at 1214 per lb. 9. 81 lb. of meal, at 134 per lb. H. 455 gal. of molasses, at 25° per gal. 10. 111 qt. of berries, at 3f& per qt. 5. 1751 doz. of eggs, at 1644 per doz. 11. 13547 yd. of cotton, at 5$ per yd. 6. 2133 lb. of pork, at 674 per lb. 12. 840 lb. of salt, at 174 per lb. REMARK.-In the following examples treat the amount of each item as a separate result, and consider 5 or more mills as 10. 13. Find the total cost of the following: 86 yd., at 1214 per yd. 591 yd., at 10$ per yd. | 1600 yd., at 1684 per yd. 93 yd., at 614 per yd. 327 yd., at 3314 per yd. 71 yd., at 50$ per yd. 150 yd., at 25$ per yd. 1141 yd., at 25$ per yd. 947 yd., at 314 per yd. REMARK. —Quarters are often written thus : 58 = 54; 171 = 171 ; 11% = 114 ; this method is not used with other fractions. 14. Find the total cost of the following: 832 yd., at 614 per yd. 1272 yd., at 1634 per yd. 713 yd., at 814 per yd. 1000 yd., at 13$ per yd. 2301 yd., at 25¢ per yd. 5473 yd., at 5¢ per yd. 28551 yd., at 20$ per yd. 8722 yd., at 50$ per yd. 624 yd., at 214 per yd. 305. To Find the Cost when the price is given and the Quantity is a Multiple, or an Aliquot part, of 100 or 1000. REMARK. – When the quantity is in even hundreds or thousands, find the cost by multiply. ing the price, expressed as a decimal, by the number of hundreds or thousands. For parts of hundreds or thousands, add equivalent fractional parts. EXAMPLE 1. Find the cost of 100 yards of cloth, at 5414 per yard. EXPLANATION.-Since 1 yard costs $.5425, 100 yards will cost 100 times as much, or $54.25. EXAMPLE 2.--Find the cost of 300 yards, at 1714 per yard. EXPLANATION.—Since 1 yard costs $.175, 100 yards will cost $17.50, and 300 yards, or 3 times 100 yards, will cost 3 times $17.50, or $52.50. EXAMPLE 3.–Find the cost of 1000 yards, at 832€ per yard. 94 EXAMPLES FOR PRACTICE IN SPECIAL APPLICATIONS. EXAMPLE 4.—Find the cost of 15 yards, at $1.374 per yard. EXPLANATION.—Since 1 yard costs $1.75, 1000 yards will cost $1750 : 250 yards, or of 1000 yards, will cost of $1750, or $437.50. EXAMPLE 6. PARTS OF PARTS.— What will be the cost of 1426 bushels of wheat, at $1.374 per bushel ? EXPLANATION.–At $1 per bushel, 1426 bushels will cost. $1426.00 25¢ per bushel, 1426 bushels will cost.. 356.50 At š = (1 of 1), or 124 per bushel, 1426 bushels will cost 178.25 At $1.374 per bushel, 1426 bushels will cost $1960.75 EXAMPLE 7.—What is the cost of 824 yards of cloth, at $1.75 per yard ? EXPLANATION.–At $1 per yard, 824 yards will cost $824.00 At * = 50° per yard, 824 yards will cost- 412.00 25$ per yard, 824 yards will cost 206.00 At $1.75 per yard, 824 yards will cost. $1442.00 At i At 1 EXAMPLE 8.–At 554 per lb., what will be the cost of 146 lb. of gunpowder ? EXPLANATION.–At $1 per lb., 146 lb. will cost. $146.00 50¢ per lb., 146 lb, will cost-.-.-.. 73.00 (1 of 1), or 54 per lb., 146 lb. will cost 7.30 At 55° per lb., 146 lb. will cost. $80.30 At } EXAMPLES FOR WRITTEN PRACTICE. 306. Find the cost of 1. 200 lb., @ 3744. 8. 400 lb., @ 9514. 15. 2. 700 lb., @ 5114. 9. 250 lb., @ 934. 16. 3. 150 lb., @ 1434. 10. 75 lb., @ 604. 17. 4. 250 lb., @ 2134. 11. 125 lb., @ 2714. 18. ö. 1000 lb., @ $1.121. 12. 1100 lb., @ $1.421. 6. 750 lb. @ 8134. 13. 500 lb., @ 374. 20. 7. 1250 lb., @ $2.621. 14. 1500 lb., @ 1844. 21. 19. EXAMPLES FOR MENTAL PRACTICE. REMARK.—All extensions in the following examples should be made mentally, the pupil writing only the cost of each item for footing. 307. 1. Find the total cost of 516 lb., at 104 per lb. 216 lb., at 124 per lb. 484 lb., at 54 per lb. 112.) lb., at 50¢ per lb. 1000 lb., at 74 per lb. 818 lb., at 25° per lb. 2500 lb., at 8¢ per lb. 1400 lb., at 204 per lb. 3000 lb., at 114 per 381 lb., at 40¢ per lb. 1095 lb., at 333€ per lb. 125 lb., at 6¢ per lb. 711 lb., at 304 per lb. 97 lb., at 8}¢ per lb. 150 lb., at 6¢¢ per lb. lh. 2. Find the total cost of 686 yd., at 15$ per yd. 297 yd., at 254 per yd. 800 yd., at 134 per yd. 2140 yd., at 5$ per yd. 1100 yd., at 434 per yd. 959 yd., at 1634 per yd. 853 yd., at 10$ per yd. 1200 yd., at 2834 per yd. 1000 yd., at 1934 per yd. 246 yd., at 20$ per yd. 298 yd., at 50¢ per yd. 2000 yd., at 2134 per yd. 398 yd., at 30$ per yd. 931 yd., at 25° per yd. 606 yd., at 124¢ per yd. 450 yd., at 334 per yd. | 1315 yd., at 333$ per yd. 150 yd., ar 25$ per yd. 3. Find the total cost of 1400 lb., at 4¢ per lb. 9362 lb., at 12% per lb. 291 lb., at 50¢ per lb. 2168 lb., at 3}¢ per lb. 21431 lb., at 15% per lb. 14372 lb., at 25° per lb. 7000 lb., at 54 per lb. 546 lb., at 114 per lb. 19783 lb., at 33}¢ per lb. 2462 lb., at 614 per lb. 2980 lb., at 1634 per lb. 8441 lb., at 754 per lb. 5963 lb., at 83€ per lb. 593 lb., at 134 per lb. 930 lb., at 66$$ per lb. 12521 lb., at 10¢ per lb. 12502 lb., at 614 per lb. 6752 lb., at 12:14 per lb. 4. Find the total cost of 5252 yd., at 84 per yd. 367 yd., at $1.25 per yd. 2100 yd., at 75$ per yd. 11781 yd., at 9¢ per yd. 282 yd., at$ 2.50 per yd. 146 yd., at 25$ per yd. 28533 yd., at 104 per yd. 5771 yd., at 55$ per yd. 500 yd., at $.374 per yd. 1400 yd., at 614 per yd. 315 yd., at 75$ per yd. 1000 yd., at $1.874 per yd 5. Find the total cost of 832 yd., at 55$ per yd. 1272 yd., at 1634 per yd. / 20053 yd., at 64¢ per yd. 713 yd., at 75$ per yd. 500 yd., at 184¢ per yd. 1000 yd., at 8334 per yd. 1071 yd., at 504 per yd. 2693 yd., at 124 per yd. 250 yd., at 27$ per yd. 2303 yd., at 603€ per yd. 29601 yd., at 904 per yd. 931yd., at 3334 per yd. 17532 yd., at 25¢ per yd. 1832 yd., at 834 per yd. 7683 yd., at$ 1.25 per yd. 46 yd., at 154 per yd. 23753 yd., at 104 per yd. 17561yd.,at $1.124 per yd. 6. Find the total cost of 6291 yd., at 334 per yd. 250 yd., at 1334 per yd. | 55482 yd., at 14¢ per yd. 11402 yd., at 5$ per yd. 400 yd., at 151€ per yd. 1250 yd., at 7$ per yd. 5943 yd., at 6}$ per yd. 7563 yd., at 16}$ per yd. 300 yd., at 23$ per yd. 3469 yd., at 854 per yd. 13751 yd., at 20$ per yd. 500 yd., at 4134 per yd. 12912 yd., at 114 per yd. 1741 yd., at 25° per yd. 186 yd., at 16¢ per yd. 5933 yd., at 1214 per yd. 9063 yd., at 6634 per yd. 175 yd., at 15$ per yd. 308. To Find the Quantity when the Price is an Aliquot Part of $1. EXAMPLE 1.—If oats cost 3314 per bushel, how many bushels can be bought for $54 ? EXPLANATION. -Since 1 bushel costs 3334, or 1 of $1, 3 bushels can be bought for $1 ; and if $1 will buy 3 bushels, $54 will buy 54 times 3 bushels, or 162 bushels. EXAMPLE 2.-If a yard of cloth costs 6634, how many yards will $84 buy? EXPLANATION.—Since the price is of itself less than $1 per yard, the number of yards will be greater than the number of dollars expended; 1 of 84 = 42; 84+42 = 126, or 126 yards. |