10. If the carriage of 8 cwt. 128 miles cost $ 12.80, what must be paid for the carriage of 4 cwt. 32 miles ? Ans. $1.60. :11. If 16L. 18s. be the wages of 16 men for 8 days, what sum will 32 men earn in 24 days? Ans. 101L, 8s. 12. If 350 L. in half a year gain 10L. 10s. interest, what will be the interest of 400 L. for 4 years 3 An's. 96 L. INVERSE PROPORTION. RULE. Transpose the inverse extremes; that is, set that which is in the first place under the third, and that which is in the third place under the first; then work as in Direct Proportion. EXAMPLES 1. If 7 mer reap 84 acres of wheat in 12 days, how many men can reap 100 acres in 5 days? Ans. 20 men. 84 A. 100 direct Contracted. 5 12 16ø( 20 Ans. #m. $ 420 1200 12 7 力 12 D. }ım. { 7 , { 420)8400(20 Ans. 840 ! 0 2. If 4 dollars be the hire of 8 men for 3 days, how many days niust 20 men work for 40 dollars ? Ans. 12. 3. If 4 men have $ 3.20 for 3 days work, how many men. will earn $12.30 in 16 days? Ans. 3 men. 4. If 4 reapers have 12 dollars for 3 days work, how many will earn 48 dollars in 16 days? Ans. 3. 5. If 100 L. in 12 months gain 6 L. interest, what sum will gain 3 L. 75. 6d. in 9 months ? Ans. 75 L. 6. If a footman travel 240 miles in 12 days, when the days are 12 hours long; how many days will he require to travel 720 miles when the days are 16 hours long? Ans. 27 days. . 7. If 100L. in 12 months gain & L. interest, what sum will gain 8 L. 12s. in 5 months ? Ans. 258 L. 8. If 200 lb. be carried 40 miles for 40 cents, how far may 20200 lb, be carried for $60.60 ?' Ans. 60 miles. PROMISCUOUS EXAMPLES. 1. If 4 men in 5 days eat 7 lb. of bread, how much will suffice 16 men 15 days? Ans. 84 lb. 2. If 100 dols. gain $ 3.50 interest in 1 year, what sum will gain $38.50 in 1 year and 3 months ? Ans. 380 dols. 3. If it take 5 men to make 150 pair of shoes in 20 days, how many men can make 1350 pair in 60 days ? Ans. 15. 4. If the wages of 6 men for 21 weeks be 120L. what will be the wages of 14 men for 46 weeks? Ans. 613 L. 6s. 8d. 5. If 333 L. 65. 8d. gain 15 L. interest in 9 months, what sum will gain 6 L. in 12 months ? Ans. '100 L. Practice is a short method of ascertaining the value of ány number of articles, or of pounds, yards, &c. by the given price of one article, one pound, or one yard, &c. Practice may be proved by Compound Multiplication; or, by the Single Rule of Three Direct. TABLES OF ALIQUOT PARTS.* 2 * An aliquot part of a number, is any number that will divide it without a remainder ; thus, 4 is an aliquo: part of 30, and 8 of 56. A sum or quantity is an aliquot part of a greater sum or quantity, when a certain number thereof will make the greater ; thus a shilling is an aliquot part of a pound, becausc 20 shillings make one pound. When the price is less than a penny, work by RULE 1.* If the price be a farthing, or a halfpenny, divide the given number by as many thereof as make a penny, for the answer in pence. If the price be three farthings, find the value of the given number at a halfpenny, and afterwards at a farthing; then add the two results together, and their amount will be the answer. 7 When remainders occur, proceed with them as under rule 3, Compound Division. EXAMPLES. 1. What is the value of 4528 quills, at each? 2. What is the value of 4528 quills, at each? (1) (2) lilil 4528 4528 1132 value at i 12)3396 Ans.in pence. Ans.redu. 4 L. 145. 4d. 210 2813 Al * The reason of this rule may be given thus : The value of any number of articles at a farthing, or a halfpenny, &c.each, is that number of farthings, or halfpence, &c. and to find their value in pence, shillings, or pounds, we reduce the farthings, or halfpence, &c. to pence, shillings, or pounds: thus the value of 4528 quills, at a far. thing each, is 4528 farthings; which, recluced, make 4 L. 14s. 4.See example 1. . When the price is three farthing's each, the opera. tion is somewhat different; for, this being no aliquot part of a penny, we cannot divide the given number by as many thereof as make a penny, to produce pence; we are therefore obliged to use the component parts of the price; as in example 2. The explanation of this rule, with a little variation, will apply to each of the other rules in Practice. Welcon 4 12 1 L. 8. d. 6. 6812 at Answer 14 3 10 7. 1487 at 8. 4712 at 14 14 6 When the price is not less than a penny, but less than a shilling, and is an aliquot part of a shilling, work by RULE 2. Divide the given number by as many of the price as make a shilling, for the answer in shillings. EXAMPLES. 1. What is the value of 7612 lb. of rosin, at 1d. per 1b. and also at 11d. per Ib. ? | 18.1 75 | 7612 at id. | 14d. 1 i | 7612 at 1£d. 210)634 4 2|0)95f16 L. 8. Ans. redu. 31 L. 14s. 4d. Ans.reduced 47 L. lls. 6d. d. d. 2. 24 at 1. Answer 2 0 3. 3806 at 14 23 15 9 -4. 1769 at 2. 14, 14 ro 5. 7649 at 3. 95 12 3 6, 8120 at 4. 135 6 8 7. 2704 at 0. 69 When the price is not less than a penny, but less than a shilling, and is no aliquot part of a shilling, work by RULE 3. Separate the price into parts, one of which shall be an aliquot part of a shilling, and the others, either aliquot parts of this part, or of a shilling, or of one another: find the value of the given number at one or more of such parts of the price as are aliquot parts of a shilling by Rule 2; then, from the value at these parts, find the value at the rest of the price, and add the several sums together for the answer. EXAMPLES. 1. What is the value of 6192 yards of tape, at 21d. per yard? 2. What is the value of 3711 lb. of sugar, at 7 da per lb, ? Answer reduced 119 L. 168. 810. Note.-In working the former of these examples, we find the value of the given number at 2d. by Rule 2, and divide the result by 8 to find the value at }; for as 1 is an eighth part of 2d. the value at 4 must be an eighth part of the value at 2d. The latter example is wrought in a similar manner. d. 1. 8. d. 3. 3596 at 21 Answer 33 14 3 4. 1861 at 11 9 13 10 5. 7000 at 41 123 19 2 6. 781. at 5. 149 12 7. 3762 at 7. 109 14 8. 3747 at 75 117. I 104 9. 4697 at 8. 156 11 4 10. 7924 at 91 313 13 2 11. 7796 at 101. 341 1 6 12. 3064 at 11. 140 8 8 When the price is not less than a shilling, but less than two shillings, work by RULE 4. Let the given number stand for its value in shillings, at a shilling; find the value in shillings, at the rest of the price, and add the several sums together for the answer. 6 a |