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5. 18° X 3.1416.

6. R2 X 3.1416 = 153.9384; RP = 153.9384 = 3.1416 = 49; R=7. Ans. 7 yd. • 7. Let x = circumference; then, from 4,

12.5664 198.95; 22 = 198.95 x 12.5664 = 2500.08528; x = 50.008. Ans. 50 rd.

8. The square of the diagonal, x?, = twice the square of a side. The square of a side is, therefore, , which is the area of the square.

9. Let the pupil draw a square. On its diagonal, which may be called 150 rd., draw another square. Produce two sides of the smaller square so as to make diagonals of the larger one. An examination of the small square will show that its area is one-half that of the other, or ļof (150 x 150) sq. rd.

10-12. See 6, 7, and 1, of Measurements, Art. 1107. 13. See 4. 100 sq. ft. - 12.5664 = 7.958 sq. ft. Ans.

Area = circumference ? x .07958. 14. The altitude=V625 – 49 = 24. Area = (40 x 24) sq. rd. 15. Find the perpendicular, V1002 – 80?; etc. 16. See 10 of Measurements, Art. 1107. 17. Calculate the altitude. Area = + (60+130) x altitude. 18. See 4, Measurements, Art. 1107. 19. The altitude = V30- 15.

20. Find the area as in 1, Measurements, Art. 1107. Divide the area by one-half the base to obtain the altitude.

21. Area = 800 sq. rd.; area of the square constructed on its diagonal = 800 sq. rd. X 2= 1600 sq. rd. ; length of the diagonal = V1600 rd. = 40 rd. Ans.

22. See Measurements, Art. 1107, 7, for the area of one of the six equal triangles.

23. (62 X 3.1416) sq. in.

24. Its area is one-half the area of the square constructed on the diameter; that is, te of 100 sq. ft.

25. The area of the sector is that of the circle. Area of circle = 100 * 3.1416.

1125. 2. See Supplement for the definitions.

3. $6.75 is what per cent of $2700 ?

6. The note is due April 13 (10), 1891; the term of discount is 102 (99) da.

$261. 7. Do not place the rate under the principal. 6% 15.66 See Arithmetic, Art. 983, 27.

$276.66 8. Make the divisor a whole number, 68702050000 --- 48665. See Art. 1007, 7.

9. To yield 47%, the bonds must have a face value of $225 - .045=$5000. Their cost will be $5000 x 1.0525.

10. See Art. 1051, 10. 1126. 10. 734 mi. - 21. 11. See Art. 1056.

12. $3 x 4x4• . Teachers should not require pupils to use pencils unnecessarily. See page 5.

16. +68+4 = x.
18. See Arts. 546 and 1022, 15.

19. (of[(14+ 16 + 14+ 16) X 8] =-11) -- 24. Cancel. The perimeter of the room multiplied by the height gives the surface of the walls ; } of this gives the number of square feet remaining after the openings are deducted; dividing by 17, gives the number of feet of paper needed ; dividing by 24, which is the number of feet in a roll, gives the number of rolls, or 115. As a part of a roll is not obtainable, 12 rolls must be purchased.

1127. 5. Cellar contains (10 x 8 x 2) cu. yd.
6. (48 X 32) = (16 x }).
9. See Art. 1100, 19.

1128. 7. 16:20 :: 2:25. See Arts. 1068-1073.
13. fo of of $18000. Cancel.
14. $ 120 = 570
15. Rate, $8 per $ 1000.
1129. See notes on previous Special Drills.

1131. 44 x 22 = (44 x 20)+(44 x 2); 44 x 18 = (44 x 20) - (44 X 2). 26 x 62 = (26 x 60)+(26 x 2); 26 x 58=(26 x 60) – (26 X 2).

1133. See Art. 1064. 49 x 49, Art. 1032.

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1135. See Art. 1044. The mark on each case is H. B. The numbers of the cases are 5453 and 5454. The goods are sent (consigned) to Messrs. Hamburger Bros., to be sold on commission.

944 yd. at 2s. 3d. £10 12s. 74d. 140% yd. at ls. 9d. 12 6 37

61 yd. at 3s. Od. 9 3 0 348 yd. at ls. 9d. 30 9 0

£62 10 117 Less to, 1 11 34

£60 19 8 The value in U.S. money = $296.78. Ad valorem duty at 50% = $148.39. Specific duty (295 lb. + 351 lb.) = 646 lb. @ 44¢ = $284.24. The entire duty = $ 432.63. Ans.

1137. Divide area by 1 base. See Art. 1107, Measurements, 1 and 4.

1139. 1. A's equivalent = 72, (6 x 12); B's= 70, [(5 x 11) +(3 x 5)]. Total, 142. A pays hoe of $175; etc. · 2. Total debts ($ 750 +$ 1125 +$1245) = $3120.

3120 : 750 :: $ 1287: A
3120 : 1125 :: $1287 : B

3120 : 1245:: $1287:0 3. K, 50 x 26; L, 60 X 26; M, 70 x 20; N, 90 x 22; etc.

4. Some persons prefer to employ smaller figures for the capital invested, by dividing each by the same number. A's can be taken as $25; B's as $40; and C's as $50; or $5, $8, and $10 may be used.

5 x 12= 60
8 x 9= 72
10 x 5 = 50

182: 60 :: $15000: A's share.
182 : 72::$15000 : B's share.
182: 50 :: $15000 : C's share.

5. Counting each ox as 3 sheep,

60 x 10 = 600
50 x 8= 400 1000
75 X 8= 600
30 X 7=210 810
54 x 10 = 540
10 x 12 = 120 660
90 x 12= 1080

3550 : 1000 :: $152.50 : W
3550 : 810 ::$ 152.50 : X
3550 : 660 :: $ 152.50 : Y

3550 : 1080 :: $ 152.50 : Z 6. 220 yd. were built in 11 da. by 18 men. 480 yd. will be built in 18 days by ? men. 18 men x 11 x 480_0

V=24 men. 6 extra men. Ans.
220 x 18
7. See Art. 1122, 1.

8. 14 men in (84 x 12) hr. mow 168 acres. 20 men in (74 x 11) hr. mow ? acres.

NOTE.— A thoughtless scholar will sometimes fail to see that the 15 min. should be joined to 8 hr.; he will, therefore, compare 8 hr. with 7 hr., and 15 min. with 48 min.

9. To do 4 times the work in of the time will take 20 times 12 men, or 240 men. (Omit 20 da.)

10. At the time they meet the sinking vessel, 60 men have provisions for 24 da. ; these will last 72 persons 20 da.

72:60 :: 24 da. : x 11. Omit the dimensions of the boards. If 76 are worth $19.76, 50 are worth $19.76 x 50 = 76.

1140. This table will furnish some practice in addition and division, and should not be passed over.

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