Equations in this book are intended to give aid in solving the more difficult problems of arithmetic, and are not given as exercises for their own sake. To keep within the limits of arithmetic such arithmetical problems or equations as, "Find two numbers whose sum is 10 and whose difference is 2," or X x + y = 10 should be solved by eliminating by addition or subtraction the unknown number found in the negative term or terms, if there 3 x 2 y 3 Sy+2x=18 { 25. 26. { 2y-3x=5 5y+4x=93 S4x-7y=12 3x+5y=50 y = 1, and 2+2 = 4. Multiplying the members of each equation by the 1. c. m. of the denominators in that equation will clear the equation of fractions. SUGGESTION. 9x; 6 times = 2y; 6 times 1 = 6. members of the first equation by 6, then, changes it to 9 x Find two numbers related to each other as follows: = 34; = 20. 33. Sum of 2 times the first and 3 times the second sum of 2 times the first and 5 times the second = 50. 34. Sum = 18; sum of the first and 2 times the second 35. A grocer sold 2 boxes of raspberries and 3 of cherries to one customer for 544, and 3 boxes of raspberries and 2 of cherries to another for 56¢. Find the price of each per box. 36. A druggist wishes to put 500 grains of quinine into 3grain and 2-grain capsules. He has 220 capsules. How many capsules of each size can he fill? 37. On the Fourth of July, 850 glasses of soda water were sold at a fountain, some at 5 each, the others at 10 each. The receipts were $55. How many were sold at each price? 38. A fruit dealer bought 36 pineapples for $2.50. He sold some at 12 each and the rest at 10 each, thereby gaining $1.50. How How many did he sell at each price? 39. An errand boy went to the bank to deposit some bills for his employer. Some of them were 1-dollar bills, and the rest 2-dollar bills. The number of bills was 38 and their value Find the number of each. was $50. 40. A man noticed that a 15-word day message by telegraph cost him 40 and a 22-word day message 54, between the same two cities. Find the charge for the first ten words and for each additional word. 41. When 2 baskets of Delaware peaches cost 15 more than 3 of Whitestone peaches, and 3 baskets of Delaware peaches cost 45 less than 6 of Whitestone peaches, what is the price of each per basket? 42. At a factory where 1000 men and women were employed, the average daily wage was $2.50 for a man and $1.50 for a woman. If labor cost $2340 per day, how many men were employed and how many women? 43. The receipts from 300 tickets for a musical recital were $100. Adults were charged 50 ₫ and children 25, each. How many tickets of each kind were sold? 44. It required 60 inches of tape to bind the four edges of a card on which a photograph was mounted. The length of the card was 6 inches greater than the width. How many inches long was the card? how many inches wide? 45. A lieutenant of the U. S. navy received $150 per month while on sea duty and $127.50 per month while on shore duty. A lieutenant's salary for a year amounted to $1620. How many months was he on sea duty? on shore duty? 46. The great columns of Bedford stone in the Indianapolis postoffice building weigh 94 tons each, including the shafts and the capitals resting on them. Each shaft weighs 74 tons more than its capital. Find the weight of a shaft; of a capital. 47. The receipts from a football game were $700. Admission tickets to the grounds cost 50, and to the grand stand, 25¢ in addition. If twice as many persons had purchased tickets for the grand stand, the receipts would have been $ 800. How many tickets of each kind were sold? 411. 1. DENOMINATE NUMBERS REVIEW EXERCISES Give these tables: liquid measures; dry measures; avoirdupois weight; troy weight; time measures; circular neasures. 2. How many feet are there in 220 yards? in 96 inches? 3. What part of a gallon is 3 quarts? 5 pints? 4. How many quarts are there in 2 bushels? in 21 pecks? 5. Reduce 4 T. 5 cwt. to tons; to pounds; to hundredweight. 6. What part of an ounce is 10 pennyweights? Find the weight of a dozen silver spoons, each weighing 10 pwt. 7. Reduce 12 minutes to seconds; to a decimal of an hour. 8. Reduce 3° 45′ to degrees; to minutes; 150" to minutes. 9. What part of a right angle is 45°? 22° 30'? 30°? 60°? 7. Reduce 14,420 pounds to tons and pounds. 8. Reduce 30,000 seconds to hours and minutes. 9. What part of 360° is 67° 30'? 86° 24'? 7° 12'? 10. What part of a ton is 4 cwt. 80 lb.? 16 cwt. 25 lb.? Reduce: 11. 150 qt. 1 pt. to pints. 12. 2000 min. to hours. 13. 15,136 pounds to tons. 14. 275 ft. 10 in. to inches. 15. 365 days to weeks, days, and hours. 16. of a right angle to degrees and minutes. 17. 11,225 feet (height of Mt. Hood) to miles and feet. 18. Add 2 T. 5 cwt.; 1 T. 12 cwt.; 4 T. 15 cwt.; 3 T. 8 cwt. 19. Subtract 3 T. 17 cwt. from 10 T.; 22 T. 14 cwt. from 25 T.; 17 lb. 11 oz. from 42 lb. 20. Multiply 12 ft. 8 in. by 6; 2 yd. 27 in. by 4. 21. Divide 85 ft. 8 in. by 4; 181 ft. 8 in. by 7. 22. How much less than a right angle is 77° 42'? 23. How much less than 2 right angles is 154° 28′ 33′′? 24. Find of 16° 32' 30''; of 16° 32' 30"; § of 125 ft. 4 in. 25. Find 5 times 11 lb. 10 oz. (av.); § of 11 lb. 10 oz. (av.). Find the time from to-day to the following dates: 26. Jan. 1, 1920 27. Feb. 8, 1915 32. The leakage 28. 29. Sept. 21, 1925 30. Oct. 28, 1918 from a 63-gallon hogshead of rock candy sirup was 2 qt. 1 pt. How much sirup remained? 33. If a skillful operator stamps the name on 24 gross 4 dozen pens per hour, how many will he stamp in 9 hours? 34. A man picked 94 bu. 2 pk. of cranberries in 12 days. What quantity did he pick per day, on the average? 35. My watch runs 36 hours after being wound. How many times must I wind it during April? 36. The balance wheel of a watch should make 5 oscillations per second. How many is that per hour? 37. If the balance wheel makes 17,985 oscillations per hour, how many minutes and seconds will the watch lose in a week? |