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?

The length of the
How many inches

44. It required 60 inches of tape to bind the four edges of a card on which a photograph was mounted. card was 6 inches greater than the width. 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?

DENOMINATE NUMBERS

227. To ascertain the quantity of anything, or to measure it, is to find how many times it contains some established unit of the same kind, called the unit of measure.

Thus, to measure the water in a tank is to find how many times the whole quantity of water in the tank contains some unit of measure, as 1 gallon or 1 barrel, or perhaps 1 pound or 1 ton.

228. A concrete number in which the unit of measure is established by law or custom is called a denominate number.

10 feet is a denominate number; also 10 feet 7 inches.

229. A denominate number is simple, if it is composed of units of one denomination; compound, if it is composed of units of two or more related denominations.

10 feet is a simple denominate number; 10 feet 7 inches is a compound denominate number.

NOTE. Tables of denominate numbers are found on pages 345-347.

REDUCTION

230. 1. How many quarts are there in 1 gallon? in 2 gal.? in 21 gal.? in 2.5 gal.?

2. In 10 quarts, how many gallons are there and how many quarts over? how many gallons and what part of a gallon? 10 qt. 2 gal. 2 qt. 2 gal. 2 qt. = 21 gal. = 2.5 gal.

231. Changing the form of a number without changing its value is called reduction.

Reduction to a lower denomination is called reduction descending; to a higher denomination, reduction ascending.

EXERCISES

232. 1. Give these tables: liquid measure; dry measure ; avoirdupois weight; troy weight; time measure; circular

measure.

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°?

WRITTEN EXERCISES

233. 1. A dealer has to put into pint bottles.

31 gal. 2 qt. of olive oil that he wishes How many bottles does he need?

Since there are 4 quarts in 1 gallon, in 31 31, number of gal. gallons there are 31 times 4 quarts (§ 68), or

4

124

+2

126, number of qt. 2

252, number of pt.

124 quarts; and in 31 gal. 2 qt. there are 124 quarts + 2 quarts, or 126 quarts.

Since there are 2 pints in 1 quart, in 31 gal. 2 qt., or in 126 quarts, there are 126 times 2 pints, or 252 pints.

Hence 252 pint bottles will be needed to hold the oil.

2. A train made a run of of a mile in 55 seconds. How many feet did it run per second?

3300 ft. ÷ 55 = 60 ft., the rate per second.

Then,

What part of a mile

1 mi. = 320 rd. = 320 × 51 yd. = 1760 yd.

11. Reduce 14,420 pounds to tons and pounds.
12. Reduce 30,000 seconds to hours and minutes.

13. What part of 360° is 67° 30'? 86° 24'? 7° 12'?

14. What part of a ton is 4 cwt. 80 lb.? 16 cwt. 25 lb.? Reduce:

15. 6 lb. 3 oz. to ounces.
16. 150 qt. 1 pt. to pints.
17. 15,136 pounds to tons.
18. 275 ft. 10 in. to inches.
19. 14 yr. 5 mo. to months.

20. 2000 min. to hours and minutes.

21. 365 days to weeks, days, and hours.

22. of a right angle to degrees and minutes.

23. 11,225 feet (height of Mt. Hood) to miles and feet.

24. My watch runs 36 hours after being wound. How many times must I wind it during April?

25. The balance wheel of a watch should make 5 oscillations per second. How many is that per hour?

26. If the balance wheel makes 17,985 oscillations per hour, how many minutes and seconds will the watch lose in a week?

27. A woman in Gloversville made 100 pairs of gloves in a week. How much did she earn at 66 per dozen pairs?

28. If one pound of corn yields 4 ounces of starch, how much starch can be obtained from a bushel of corn weighing 56 pounds?

29. An Indiana factory, running continuously, made 11,250 dozen fruit jars in 5 da. 15 hr. How many single jars did it make per day?

30. Find the value of the 312,500 great gross of brass buttons made in this country one year, at 20 per gross.

31. How many bushels of charcoal weighing 15 pounds per bushel are required to make a ton of gunpowder that is saltpeter, sulphur, and the remaining part charcoal?

32. One year 8028 gross of fountain pens were manufactured in this country. If the average wholesale value of each fountain pen was 78.94, find the value of all.

33. The tidal wave travels about 700 miles per hour. How many feet does it travel per second?

34. A stamp-canceling machine, working 1 hr. 15 min. 12 sec., canceled 13,912 stamps. Find its capacity per minute.

35. A vessel under its own steam passed through the Suez Canal in 15 hr. 45 min. The canal is 90 miles long. What was its rate of passage per hour to the nearest tenth of a mile?

36. How long will it take a torpedo to reach its mark 1870 yards away, if it travels of a mile per minute?