14. If 1 yard of cloth cost $2, what will 3 ells F. cost ? 2 x 15. If yard of cloth cost $2.25, what will 5 ells English cost? What will 5 ells French cost ? 2.25 x 1. If 12 bushels of wheat cost $15, what will 42 bushels cost? Given 12 bushels and $15. 2. If 15 bushels of oats cost $4.50, what will 75 bushels cost ? Given 15 bushels and $4.50. $4.50 X 1 3. If 12 bushels of wheat cost $15, how many bushels will $521 buy? Given 12 bushels and $15. and $52.50. = 42 bushels. 2 2 1 12 x 4. If 15 bushels of oats cost $4.50, how many bushels will $22.50 buy? Given 15 bushels and $4.50. and $22.50. 5 5. If a man travel 48 miles in 6 hours, how many miles will he travel in 56 hours at the same rate ? Ans. 448 miles. 6. If 20 bushels of wheat yield 4 barrels of flour, how many bushels will be required for 15 barrels of flour? Ans. 75 barrels. 7. If 20 bushels of wheat yield 4 barrels of flour, how many barrels of flour will 75 bushels yield ? 8. If a man travel 50 miles in 2 days, how long will it take him to perform a journey of 375 miles at the same rate ? 9. If a staff 3 feet long cast a shadow 4 feet, what will be the length of the shadow of a steeple 180 ft. high ? Given 3 ft., staff and 4 ft., shadow. Required 180 ft., steeple and ? shadow, Shadow of steeple 240 ft. 10. If the interest of $100 for one year is $6, what is the interest of $500 for the same time? Ans. $30. 11. If a man's salary amounts to $1500 in 3 years, how much will it amount to in 7 years? 12. If 124 bushels of wheat cost $15, what will 353 bushels cost ? 351 x 2 = 11 15 x 1 124 x 2 = 25 13. If ý of a barrel of flour cost $6, what will 51 barrels cost? The 51 is a multiplier and the is a divisór. 14. If 51 bushels of wheat cost $6.60, what will 371 bushels cost ? .20 6.6 xs x 112 = $44.80. 15. If 4 of an acre of land is worth $36.40, what is the value of 1515 acres at the same rate ? 151 = 283 $36.40 x x 2. 16. If y acres of land cost $1560, what will of an acre cost? Ans. $150. 17. The assets of a firm are $48576 and the liabilities $97648 ; how much will a creditor receive to whom is owing $1654? 48576 x 10543 18. If of a yard cost $27, what will 4 of a yard cost? Ans. $13. 19. If it of a ship cost £49, what is of it worth? Ans. £32. 20. What will 57 acres 3 rods and 24 perches of land cost, if 5 acres 2 rods and 6 perches cast $224.64 ? Reduce to perches. Ans. $2348.83+. 21. If $1.50 will buy 6 lbs. sugar, how much sugar will $36.50 buy? 22. If 51 yards of cloth cost $7.15, what will 721 yards cost ? $7.15 x 141 23. If 41 lbs. ham cost 87 cents, what will 354 lbs. cost? Ans. $6.79+. 24. If .75 of a ton of hay cost $15, what will 2.25 tons cost? Ans. $45. 25. If 160 acres of land cost $400, what will 830 acres cost ? 26. If I of a ship cost $4500, what will cost ? 27. If .25 of an acre of land is worth $32, what is .875 of an acre worth? 28. If 54 yards of muslin cost 46 cents, what will 201 yards cost ? Ans. 162 cents. 29. If 3 yards of cloth cost $15.75, what will 6 ells English cost ? Ans. $39.374 30. If 5 ells Fl. cost $15.15, what will 6 ells Fr. cost? In the preceding examples, the ratios were all direct; as in those cases any increase in the required term of the ratio demanded a similar increase of the unknown; but there are cases which require the ratio to be inverted, such as, the more men employed, the less time will be required to perform a piece of work; the more hours employed in the day, the less days ; the wider the material, the less yards it will take to make a garment, etc. These cases of inverse ratio are readily detected by asking this question : “Will an increase of the required term of the ratio demand an increase in the unknown term ?” If it does, the ratio is direct; but if an increase in the required term of the ratio demand a diminution of the unknown term, the ratio must be inverted; thus, PROBLEM. If 4 men can do a piece of work in 10 days, how long Will it take 8 men to do the same work ? COR.-It is evident that 8 men will do it in less time; that is, in one-half the time that it will take 4, which ratio is expressed by the diminishing ratio of 4 and 8, that is, $ = 1, in which the given term is the numerator of the ratio and the required term the denominator. EXAMPLES. 1. If 5 men can dig a ditch in 20 days, how many men will dig it in 25 days? Given 5 men and 20 days. Required, ? and 25 days. REM.-An increase in the 25 will require less men. 2. If 6 horses eat a certain quantity of hay in 30 weeks, how many horses will consume the same quantity of hay in 9 weeks? 3. If a man perform a journey in 12 days, when the days are 9 hours long, how many days of 12 hours will it take him? Given 12 days and 9 hours. ? and 12 hours. |