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25 pounds : 312 pounds : : $3.25 : the answer.
Here we first multiply the means together; we then divide the product by the first term.
Since there is a ratio between the third and fourth terms, it follows that they must be of the same denominate value. Hence, of the three quantities given, we may always take for the third term of our proportion the quantity which is of the same kind as the answer required ; then, if the answer sought is to be greater than this third term, the second term must exceed the first ; but if the answer sought is to be less than this third term, then the second term must be less than the first.
109. From what has been said and done, we deduce this first form for the
RULE OF THREE.
I. Form a proportion by placing for the third term, the quantity which is of the same kind as the answer sought; the two remaining quantities must be taken for the first and second terms, observing to take the larger of the two quantities “or the second term, when the answer sought is to exceed the third term ; but to take the smaller of the two quantities for the second term, when the answer is to be less than the third term.
II. Having written the three terms of the proportion, or, as usually expressed, having stated the question, then multiply the second and third terms together, and divide the product by the first term.
Note.—Since there is a ratio between the first and second terms, they must be reduced to the same denominate value. Also, the third term must be reduced to its lowest denomination; then the quotient found by dividing the product of the means by the first term, will be of the same denomination as the third term.
In stating questions in the Rule of Three, which quantity must be taken for the third term 3 Of the two remaining quantities, which is to be taken for the second term After the question is stated, how do you proceed to find the answer 4 Is it ever necessary to make any reduction in the terms before multiplying and dividing?
What are these reductions 3 The answer when found, will be of the same name as which term 1
1. What is the cost of 6 cords of wood, at $7 for 2 cords? 2 cords : 6 cords : : $7 : Ans. 6 2)42 Ans. $21 2. What will 9 pair of shoes cost, if 5 pair cost £2 2s. 6d. 2 5 pair : 9 pair : : £2 2s. 6d. When reduced, 5 pair : 9 pair : : 510d. 9
3. If there are 9 weeks in 63 days, how many weeks are there in 365 days? 63 days : 365 : ; 9 weeks. 9
4. If a railroad car goes 17 miles in 45 minutes, how far will it go in 5 hours? 45 minutes : 5 hours : : 17 miles. or 45 “ : 300 minutes : ; 17 “ 17 2100 300
5. If $100 will gain $7 in one year, how long will it require to gain $100? Ans. 14% years. 6. If 3 paces or common steps of a person is equal to 2 yards, how many yards will 480 paces make? Ans. 320 yards. 7. If 15 men can raise a wall of masonry 12 feet in one week, how many will be necessary to raise it 20 feet in the same time? Ans. 25 men. 8. If 7 tons of coal, of 2000 pounds each, will last 3} months of 30 days each, how much will be consumed in 3 weeks, or 21 days? Ans. 1 ton, or 2000 pounds. 9. If 9; bushels of wheat make 2 barrels of flour, how many bushels will be required to make 13 barrels? - Ans. 61% bushels. 10. If a steamboat of 242 feet in length move 15 miles in one hour, how many seconds will it require to move its own length 7 Ans. 11 seconds. 11. If a steamboat of 242 feet in length move 15 miles an hour, how many times its own length will it move in 11 hours? Ans. 3600 times. 12. A reservoir has a pipe capable of discharging 30 gallons in one minute, what time will be necessary to discharge 15 hogsheads 2 Ans. 31; minutes. 13. If a man can mow 9 acres of grass in 34 days of 10 hours each, how long will it require for him to mow 21 acres? Ans. 8; days. 14. If 100 pounds of galena, or lead ore, yield 83 pounds of pure metal, how much pure metal will 7 tons of galena produce, if we reckon 2240 pounds to the ton 7 - Ans. 13014% pounds. 15. If 12 barrels of flour are worth $54, what is the value of 42 barrels at the same rate? 12 barrels : 42 barrels : : $54 42 108 216
18. If H of a pound of sugar cost # of a shilling, how much will or of a pound cost 7 - *
In this example, our third term is # of a shilling. And since # of a pound is less than ++, we must obtain our ratio by dividing #3 by ++, which gives or x++. Multiplying the third term by this ratio, we have # of a shilling × 3% x++. To reduce this with the least labor, we must resort to the method of cancelling. Thus, cancelling the 23, which occurs in both numerator and denominator, also 13 of the numerator against a corresponding factor of the 26 of the denominator, our expression will become # of a shilling × 3 × tor- or of a shilling.
NotE.—This method of cancelling should be used when the nature of the question will admit, since it will always simplify the operation.
19. If a tree 38 feet 9 inches in height, give a shadow of 49 feet 2 inches, how high is that tree which, at the same time, casts a shadow of 71 feet 7 inches 7
In this example, our third term is the height of the first tree, which is 38 feet 9 inches=383 feet =1#5 feet: our ratio will be obtained by dividing 71 feet 7 inches=7.1% feet = ** feet, by 49 feet 2 inches=49+ feet =2#5 feet: which thus becomes * x 3% s. Multiplying the third term