Advanced Arithmetic

21. Which yields the better income, $1675 at 5% or $1375 at 6%? What is the difference for 2 yr. 6 mo.?

22. A man receives $1718.75 interest in 2 yr. 6 mo. on an investment of $17,500. What is the rate of interest?

23. A boy has $300 given to him the day he is 14 years old. His father invests it for him in a 5% promissory note, due on the day he is 21 years old. What is the amount on the day the note is due?

24. A real estate dealer buys 360 acres of farm land at $30 an acre, and after keeping it 7 months sells it at an advance of $3.75 an acre. The money being worth to him 5% a year, how much does he gain by the transaction?

25. A man having $26,750 invested in business has found that his annual profits average 18% a year. He is offered $35,000 for the business, which he can invest at 44%. If he sells out and retires, what will be his loss in income?

26. On April 10 a coal dealer borrowed $33,250 at 5%, with which he purchased his summer's supply of coal at $4.75 a ton. He sold the coal at $5.65 a ton, the buyers paying for unloading and delivery, and paid his debt on November 16. How much did he gain?

27. I own a house which I rent at $25 a month. My taxes are $50 a year, my repairs $50, and my insurance $10. Would it be better for me to sell the house for $5000 and invest the money at 4%, if my taxes would then be reduced to $10? What is the difference in income?

28. On October 15 a dealer purchased $1750 worth of goods for the holiday trade on 30 days credit. At the end of that time he gave his note for 2 months at 6% a year. He sold the goods for $2105, and paid the note when due. What per cent did he make on the original purchase price?

FACTORY PROBLEMS

WRITTEN EXERCISE

1. A certain canning factory uses the product of 75 acres of peas during the three weeks' season. In this time it puts up 48,000 cans of peas. At 6 days to the week, how many acres of peas does it use a day? How many cans does it put up every 3 hours, allowing 8 hours to the working day?

2. A-lb. stick of solder is used to seal 30 of these cans. How many pounds of solder are required for a week's work? This solder being 20% lead, how many pounds of lead are used in a day?

3. The steam kettle in which the peas are cooked will hold 3 baskets, each containing enough peas for 250 cans. How many cans of peas can be cooked in one forenoon (8 A.M. to 12 M.) if 25 min. are allowed to each kettleful?

4. A farmer owns 3 of the 75 acres mentioned in Ex. 1. He therefore furnishes the peas for how many cans? If he takes for his pay 50% of the canned goods for which he furnished the peas, how many cases of 24 cans each should he receive?

5. A workman in the factory puts together 200 of these cases a day. How long will it take him to put together cases enough for the season's output mentioned in Ex. 1? How much will he earn in that time, at 90 per hundred cases?

6. The factory runs from 8 A.M. to 5 P.M., with an hour out at noon. One day some machinery broke down, stopping all work from 10 A.M. to 2:30 P.M. What was the total output that day?

PROBLEMS OF A GROCER

WRITTEN EXERCISE

1. Mr. F. T. Barker has $20,000 invested in his building and grocery stock. Last year his profits were $2500. What was his rate of profit?

2. Of the $20,000 he owes $8000, paying 51% interest. How much did this take from his $2500 profit? What rate of income is

he receiving on his own money?

3. Last summer he bought 100 muskmelons for $6.50. He sold half of them at 9 each, 33 of them at the rate of 3 for 25g, and the rest he had

to throw away. Did he gain or lose, and what per cent?

4. He bought 300 bananas for $4 and sold them at the rate of 22 a dozen. What was his gain per cent? At 25¢ a dozen, what would it have been?

5. He bought 500 lb. of clover honey for $70 and sold all but 50 lb. of it at a profit of 32%. The rest he sold at a loss of 55%. Did he gain or lose, and how much?

6. He employs 4 order clerks, paying them $12 a week and 1% commission on all goods sold. Their average sales being $280, $220, $240, and $270 a week respectively, what is the average weekly income of each?

7. He buys sugar at $20 per barrel of 344 lb., and sells it at 6 a pound. How much does he gain on 135 lb.?

8. If he can sell a barrel of sugar (see Ex. 7) at the rate of 48 for 7 lb., how much will he make on a barrel?

9. If he buys a 45-lb. chest of tea for $16.20, and sells it at 50% a pound, what is his rate of profit?

10. If 12 chests of the above tea were damaged by being stored in a damp place, and brought 25g a pound, what was the loss? What was the per cent of loss?

11. He bought coffee by the 100-lb. bag at $20 a bag. At what price per pound must he sell this to make 45%?

12. If he buys flour at $4.75 a barrel and sells it at $5.25, what profit does he realize on 51 bbl.? What is the per cent of profit?

13. He pays $4 a box for laundry soap, 100 cakes to the box, and sells the soap at 6 cakes for a quarter. What is his gain on a dozen boxes? his per cent of gain?

14. He bought 15 boxes of starch at $1.60 a box. There being 40 lb. to the box, what is his gain if he sells it all at 5 a pound? What is the rate of gain?

15. He bought 9 cases of tomatoes, 2 doz. cans to the case, at 92 a dozen. He sold them at 3 cans for a quarter. What was his gain or loss? the per cent of gain or loss?

16. A box of condensed milk contains 4 doz. cans. he buys 18 boxes at $3.84 each, and sells at 7 a can and the rest at a profit of 121%, does he gain or lose on the lot, and how much?

17. He buys 100 5-lb. caddies of Hyson tea for $420. He sells 75 caddies at a profit of 15%, and the rest at a loss of 5%. How much did he gain? At what price apiece I did he sell the 25 caddies?

RATIO AND PROPORTION REVIEWED

ORAL EXERCISE

1. What are the two common ways of expressing the ratio of 3 to 5 ? Write them on the blackboard.

2. What must be the nature of the terms of a ratio, as to similarity? Illustrate.

3. In the ratio 4 ft. : 20 ft., which term is the antecedent? What is the name of the other term?

4. What does the ratio of $4 to $2 equal? of 4 ft. to 2 ft.? What is the nature of the ratios of concrete numbers?

State the simplest values of the following ratios:

5. 2.

10. 38.