desires to start at once with his x, without any preliminary calculations; and the usual method of treating these examples requires him first to ascertain the gain or the loss before commencing his equation. The formula employed in the first five examples is: = gain or loss. Cost x rate When the pupil knows any two of these three terms, he can calculate the third; and 6-15 furnish data from which the necessary two items can be obtained. The pupil must, however, be careful in 11, for instance, not to subtract the loss from the selling price to obtain the cost. In the following equations, cost x * is made equal to the gain or the loss. No canceling has been done. 6. 600 x = 18; 6 x = 18. 7. 1203 x = 401. 100 100 100 100 10. 17 100 13. 100 10. 34.x = 5.25 ; 84 x = 525. 13. 875.x = 43.75; 875 x = 4375. 14. 934.56 x – 16 100 In 16-20, the cost is represented by x. 16. 2+ = 468.75. 18. 2+ = 1646.08. 17. . - = 73.84. 19. « - 160 = 204 14. 15. 1012.00 X = 168 75 100 7. 19. 871. In 1, the 30 cu. yd. are reduced to cubic feet by multiplying by 27. Instead of performing the different multiplications, they are merely indicated, so that work may be saved by canceling. Although 2 should be a simple problem for a bright pupil, it is apt to prove puzzling unless an x is introduced. A pasteboard box may be used to represent the walls and the ceiling of a room, the sides and the top being then opened out to permit of its representation on the blackboard. 3. The area in square feet = 1 of 132 x 110. This is reduced to acres by dividing by 9 x 304 x 160. 132 x 110 x 4 == Ans. 2 x 9 x 121 x 160 4. Number of strips = 6 yd. - 27 in. = 6 yd. - fyd. = 6 x 7. The “ development” of the fence will be represented by four adjoining rectangles, each marked 6 ft. high, the lengths being 25 ft., 100 ft., 25 ft., and 100 ft., respectively, the whole forming a rectangle 6 ft. X 250 ft. 8. A board's area in square feet = 12 X 1 =6. Dividing number of square feet in the fence by 6, gives the number of boards. 9. The cost of a square foot is obtained by dividing $181.50 by (160 X 304 x 9); this, multiplied by (300 x 200), gives the cost of the plot. $181.50 X 4 x 300 x 200 160 x 121 x 9 The amount received for the lots will be $160 X 6. 10. Number of cakes = (320 x 160) =(4 2). 11. Number of cubic feet = 320 x 160 x 14. 12. (320 x 160 x 11) - (15 X 32). 13. Number of square feet originally = 640 x 440. For building purposes, there will be four pieces, each measuring 300 ft. by 200 ft. 14. The difference between the above areas will represent the number of square feet in the streets. 872. Many of these exercises can be used for mental and sight work. For methods of solution, see Art. 870. 873. As a preliminary to the formal study of interest, the teacher will need to see that her pupils understand what is meant by the term. She can explain that a person borrowing money should pay for its use, just as a person who rents a house, etc. 874. In changing 4 mo. 10 da. to the fraction of a year, many teachers prefer to reduce the time to days and to write the result over 360, 88, leaving the reduction to lowest terms for the subsequent cancellation. In the same way, 1yr. 5 mo. 15 da. is changed to (360+ 150+15) da., or 525 da. = yr. The reduction to days is done very rapidly. 875. 1. $ 750 X 16 XZ. 5. $ 360 X 167 X 2. $ 84.75 X 140 x 19. 6. $ 94.43 X 100 X 300 3. $308.25 x 80 x 36%. 7. $ 400 x 280 x 48. 4. $464.75 x 16 x . . etc., etc. 877. The teacher should explain that a person that owes money, frequently gives a note as an acknowledgment of the debt, etc. 878. There is no general method applicable to these problems. 1. Interest for a year is $12, or $1 per month, which gives $ 19 for 1 yr. 7 mo. 2. $ 3.60 per year is 1¢ per day, 33¢ for 33 da. 5. If $ 50 produces $6 in 2 yr., it will produce $3 in 1 yr.; rate, therefore, is 6%. 6. $ 18 per year is $1 for 20 da., or yr. 8. 4% per year=1% for 90 da. ; 1% of $ 150 = $ 1.50. 9. 5% per year = {% for 36 da. ; 1% of $240 = { of $2.40. 11. $1 is 100% of $1; at 5% per year it will take 20 yr. to make 100% 12. At 6% it will take 16s yr., or 16 yr. 8 mo., to make 100%. 13. Disregarding $14.90, it will take 25 yr. at 4% to make 100%. 14. 1% per month = 8% for 16 mo. ; 8% of $90 = $ 7.20. 15. 5% for 360 da. =1% for 72 da. 16. 360 da. =-41 = 720 da. 9= 80 da. 17. 5% for 1 yr. = 1% for 72 da. ; 1% of $ 75= 75 cents. 18. 1% of $ 63. 20. 1% of $840. 22. 1% of $ 275. 19. 1% of $ 570. 21. 1% of $ 150. 23. 2% of $360. 3. 3 mi. 96 rd. = 1056 rd. ; 3 hr. 16 min. = 34 hr.; 1056 rd. x 34 = 1056 rd. x 45 = 17448 rd. = 3449 rd. = 10 mi. 2493 rd. Ans. 4. (+) x (* *17) - (X 84) = 12 x * X X { x = 1. Ans. 8. The first two figures express 1800; the second two, 5.4. 22. $48.37 = 81. 880. 2. Provisions that will supply 450 men for 5 months will supply 5 times 450 men for 1 month, and will supply (5 times 450 men) - 9 for 9 months, or 250 men. The number that must be discharged = 450 men - 250 men = 200 men. Ans. 15. : de 100 100 16. D bought X4 X5 X & of the ship. 18. 100 x + 50x = 340 x 75. 19. x= number distributed by each new man; 2x= number distributed by each experienced man. 16x + 32x = 36000. 20. «- * = 1972.65. 881. 10. 100 cents -- 1.13. 883. 3. $1.10 + 15% of $1.10." 4. 9876 – 87+45 9876 = 87.x + 45. 5. 640 is what per cent of (640 +560), etc. 6. 43 gal. 3 qt. 1 pt. = 437 gal. ; $ 70.20 --437 = Ans. 7. (48 X 32) = (16 x 3). 8. 20 is what per cent of 160 ? 20 is what per cent of 180 ? 10. Selling price per bbl. = :- 600 7: 46% * 600 24 Let <= cost per bbl. «- * |