8. The same savings bank organized a Ten Cent Club (see problem 7), which pays 10¢ the first week of the year, 20¢ the second week, and so on. How much does a member of this club pay in dues in 50 weeks? of 50 weeks?

How much should he receive at the end

9. What is the purpose of sending a letter special delivery? What postage, in addition to the regular postage, is required? What is the cost of sending a special delivery letter weighing 1 oz.?

10. It is estimated that skim milk for feeding purposes is worth half as much per 100 lb. as corn is worth per bushel. What is 200 lb. of skim milk worth when corn is worth $0.90 a bushel? 50 lb. of skim milk? 60 lb.? 80 lb.?

II. Pigs just after weaning should be fed about 5 lb. of skim milk with each pound of corn. What is the skim milk worth which should be fed such pigs with each bushel of corn, when corn is worth $0.80 a bushel and 100 lb. of skim milk is worth half as much as a bushel of corn?

12. Dorothy saved 36¢ one week, 48¢ the second week, 51¢ the third week, and 45¢ the fourth week. What were her average savings for the four weeks?

13. The rainfall at New Orleans for the first six months of a recent year was: 4.6 in., 4.5 in., 5.3 in., 4.9 in., 3.9 in., and 6.2 in. What was the average rainfall at New Orleans for these six months? Answer correct to the nearest .01 in.

14. To find the standing of a baseball team, divide the number of games it won by the number it played, computing the result to the nearest thousandth. What is the standing of a baseball team which won 88 games in a season and lost 52? which won 75 and lost 51?

15. The batting average of a player is found by dividing the number of hits he made by the number of times he was at bat. Find the batting average of a player who was 422 times at bat and made 132 hits. Reckon the average to the nearest .001.

16. The postage on newspapers and periodicals is 1¢ for each 4 ounces or fraction thereof. What is the postage on a package of newspapers weighing 12 oz.? 6 oz.? 10 oz.? 9 oz?

17. Find out the meaning and purpose of registering a piece of mail. What is the cost?

18. If a carpenter who is earning $2000 a year puts $120 of this in a savings bank, what decimal part of his earnings does he put in the savings bank?

19. Mildred's father has an income of $3000 a year. He sets aside .25 of this for food, .20 of it for rent, .15 of it for clothing, .15 of it for operating expenses, .15 for savings, and the remainder of it for amusement, church, charity, etc. How much money does he set aside for each?

20. A farmer in northern Michigan grew 2700 bu. of potatoes on 12 acres of land for which he paid $12.50 an acre. He sold the potatoes at $0.80 a bushel. How much money had he left from the sale of the potatoes after paying for the land?

21. The postage on miscellaneous printed matter, weighing 4 pounds or less, is 1¢ for each 2 ounces or fraction thereof. What is the postage on a package of address tags weighing 8 oz.? weighing 5 oz.? 1 lb.? 20 oz.?

22. Be prepared to tell the class what matter may be sent parcel post, and what the rates are for parcels sent not more than 50 miles from the office of mailing. (See Book Two, pages 191, 192.)

23. What should be paid a plumber for 6 hours' work if he charges $7.20 per day of 8 hr.?

24. The number of cows in Wisconsin in a recent year was 1,819,000, and the production of milk per cow averaged 4926 lb. Estimating the value of the milk at $2.82 per hundredweight, what was the value of the milk produced in Wisconsin that year?

25. Reports from 150 New Jersey poultry farms show that in a recent year the average receipts per hen were $3.82 and the average current expenses, not including the operator's labor, were $2.34 per hen. How much more were the receipts than the expenses on one of these farms which maintained a flock of 760 hens?

26. Authorities on stock feeding estimate that 1 lb. of corn will produce .1 of a pound of beef or .2 of a pound of pork. At this estimate, how many pounds of corn are required to produce 100 lb. of beef? 100 lb. of pork?

27. In a recent period of five years, bran rose from $27.91 to $50.23 per ton. What was the increase per 100 lb. during this period, correct to the nearest cent?

28. How much more is paid a year (52 wk.) by renting a room at $3.50 a week than by the month at $12.50 a month?

29. The following is from the Portland (Oregon) Journal: "Two prune cuttings from his home in France were planted in 1857 by a French immigrant on his brother's ranch near San Jose. This was the beginning of the California prune industry, which to-day yields an annual crop of 225,000,000 pounds.' How many tons (2000 lb.) are there in this annual crop?

30. It is estimated that in a recent year 29,000 tons of commercial fertilizer were used in Lancaster County, Pa., and that the average amount used on each acre was 290 lb. At this estimate, on how many acres was it used, and what was the cost if the fertilizer averaged $34.75 per ton?

CHAPTER II '

LETTERS AS NUMBERS

SIMPLE OPERATIONS WITH LETTERS

1. In arithmetic how many different figures are used to write numbers? Name all the figures used.

2. What are the four simple operations in arithmetic?

3. What is the answer to the addition operation called? to the subtraction operation? to the multiplication operation? to the division operation?

4. Without working out, how do you indicate the sum of 6 and 2? the difference? the product? the quotient?

5. In addition and subtraction operations the numbers added or subtracted are called terms. What is the sum of the two terms 7+5? What is the sum of the three terms 8+4+2? What is the difference of the two terms 9-5? of 12-7?

6. Without working out, indicate the sum of 3 and 2; 7 and 5; 8 and 4; 9 and 3. Indicate the difference in each case also.

7. Letters are sometimes used to represent numbers. For example, w may represent the number of ounces in the weight of a candy box. Indicate the number of ounces in the weight of the box and 8 oz. of candy.

8. If n represents a number, what represents the number that is 1 greater than n? 2 greater than n? 10 greater than n?

9. If I represents one number and w another, what represents their sum?

10. What number is represented by 1+w, when I represents 4 and w represents 2? when l=5 and w=3? when l=10 and w=5?

11. If m represents one number, n another, and p another, what represents their sum? What is their sum if m=3, n=2, and p=1?

12. If n represents a number, what represents the number that is 1 less than n? 2 less than n? 5 less than n? a less than n?

13. What number is represented by n-1, when n=2? when n=3? when n=10?

14. When x=6, y=4, and z=1, what number is represented by :

15. If one boy weighs p pounds and another q pounds, what represents their combined weight? If the one weighing p pounds is the heavier, what represents the difference of their weights? If the one weighing q pounds is the heavier, what represents the difference of their weights?

16. What is meant by the factors of a number? Illustrate.

17. If a stands for 5, what does 2Xa represent? 2xa is usually written 2 a and read two a.

18. What number is represented by 2n when n=3? when n=4? when n=5? when n=10? when n=12?

19. If x cents represents the cost of a quart of milk, what represents the cost of 4 qt. of milk? 8 qt.? 16 qt.? 3 gal.?

20. If a train runs r miles an hour, how far will it run in 4 hr. at the same speed? in 8 hr.? in 12 hr.? in 24 hr.? in 2 days?

21. What number does IXw represent, when 7-10 and w=4? when 1=20 and w= = 10?.