Or, the problem may be solved as follows (Arithmetic, Art. $36 × 212.50 × 40 _ $36 × 212.50 × 204 300 x 20 300 x 20 x 5 5. The date not being given, the number of days is taken as 120+3. The proceeds for 120 da. = $490. 8. The interest on $635 for 205 da. at 5% = $18.08. Amount = $635+$18.08 $653.08. = 1115. XVII NOTES ON CHAPTER FOURTEEN 1. The total interest on the given sums of money is equal to the interest of $3000 for 1 mo. As the total sum is $1000, the interest of $3000 for 1 mo. equals the interest on $1000 for 3 mo. 1116. 3. Since the time is required, the products may be expressed in years (or months or days), and their total divided by the total of the multipliers. 5. [(15 da. ×200) + (30 da. × 300) + (45 da. × 400)] ÷ (200 + 300+400). 6. [(1 mo. x 210) + (2 mo. x 210) + (3 mo. x 210)+(4 mo. X 210)] ÷ 840. Since the sum due at each period is the same, the 210 may be omitted; (1 mo. + 2 mo. + 3 mo. + 4 mo.) ÷ 4. 7. [(2 mo. × 320) + (4 mo. × 160) + (5 mo. × 240)+(6 mo. × 240)] = 960. Or, (2 mo. x) + (4 mo. × ) + (5 mo. × 1) + (6 mo. × 4) 4 mo. Ans. 8 15 8. (2 mo. x)+(3 mo. × §) + (4 mo. × 1) + (12 mo. ×1) 71% mo. = 7 mo. 26 da. Ans. 9. (0 mo. x)+(3 mo. x)+(6 mo. x ) + (9 mo. x ) 4 mo. Ans. = 10. [(0 da. × 300) + (30 da. x 800)+(60 da. x 1000)] + (300 +800+1000) 40 da. July 1 + 40 da. Aug. 10. Ans. = 1117. 11. The total amount received number of bushels sold average price. = The arrangement of the work may follow that given in Art. 1116, Problem 3. 12. The first puts in the equivalent of 180 cows for a week; the second, 120 cows for a week; the third, 180 cows for a week; a total of 480 cows for a week. The first should pay 188 of $84; the second, 120 of $84; the 480 third, 188 of $84. Proportion is commonly employed in working examples of 15 x 12 = 180 480 180 $84: x this kind. As the whole number for a week (480) is to the first man's number for a week (180) so is the whole rent ($84) to the first man's share (x). The second proportion is used to ascertain the second man's share (y); and the third, to ascertain the third man's share (z). B 2000 x 2 = 4000 1000 × 1 = 1000 5000 13. A furnishes $2000 for 2 yr. and $1000 for 1 yr., which is the equivalent of $5000 for a year. furnishes the equivalent of $6000 for a year. The total is $11000 for a year, and the profits of $1100 3000 x 2 = 6000 11000: 5000: $1100: A 11000 6000: $1100: B are distributed in the ratios of 5000 and 6000 11000 11000, as indicated by the proportions here given. A receives $500 of the profits and his capital of $3000, or $3500 in all. B receives $3600. 15. (60 xx)+(50 × 80) = 52 (x +80). 60x400052x+4160; etc.; that is, x bu. @ 60¢ +80 bu. @ 50¢ = (x + 80) bu. @ 52¢. 16. A does = in 1 da. in 1 da.; B does in 1 da.; both do They finish the work, therefore, in 12 da., and in 1 da., in 12 da. he does 1, and A does receive $60. If 17. C's capital of $4000 for yr. may be considered as $2000 for a year. This, with $4000 furnished by A and B, makes the capital $6000. A takes 1500, or of the profits; etc. See 13. 6000' 180 tons : A's share. 600 105 180 tons : B's share. 19. Let x = number of quarts of water, then 40 — x = number of quarts of milk. 40 quarts of the adulterated article at 5¢ per quart = 200¢. (40-x) quarts of milk at 6 per quart= (240-6x). x quarts of water cost nothing. The can contains 6 qt. water and 331 qt. milk. 1120. 1. $999 rent for 1 yr. 10. mo. 6 da., or 22 mo. rent for 1 mo. 5 = $999 ÷ 221 = $999 × 11; for 12 mo. = The = $999 of 55121; 55 x = 12100; x= = 220. 3. The field contains 1600 sq. rd.; each side measures 40 rd., or 220 yd.; etc. 4. A solves 20 per hour; B solves 15 x 8, or 16, per hour; both solve 36 per hour. To solve 100 will require (100364) hours. 6. Six faces, each containing (15 x 15) sq. in. 7. Cost 90. See Arithmetic, Art. 924, 7. Selling price = 90 × 1.431. Apr. 15, 1865; Feb. 12, 1809. Ans. 8. March 4, 1861, +4 yr. 1 mo. 11 da. Apr. 15, 1865, 56 yr. 2 mo. 3 da. = 9. The selling price, $4.50 90% of cost; the latter is, therefore, $5 per barrel. Loss per barrel, 50; on 50 bbl., $25. A profit of 6% = 30 per barrel; the gain on 100 bbl. = $30. Net gain = $5. Ans. 10. 60% of 66% 40%. If 4 of a number = 810, the number = 810 × 100 = 2025. NOTE. - Observe the difference between this example and 8 of Art. 1101. 1121. 1. Having used of = 14 box. If 14 box = $17, a $9.52. Ans. box, the remainder = } of box box = $17 × 14: = 68 × 14 = 3. The 40-ft. ladder forms the hypotenuse of two rightangled triangles; CE and DE, Arithmetic, Art. 1250, Problem 9. CA, one perpendicular, measures 21 ft.; DB, the other, measures 33 ft. AB is the width of the street. AE √40-212; EB = √40-332; AE÷EB = AB. = 4. 16 oz. 12 oz. :: $28: x. 5. A partnership is the association of two or more persons for the transaction of business on joint account. One advantage of a partnership is the employment of a larger capital, with a smaller percentage of expenses than would be the case were each member to establish a separate business. The firm obtains the combined business experience of its several members, and can |