MIXED PROBLEMS.

109. 1. The area of a map laid down on the scale of an inch to a mile is 4 sq. ft. 4 sq. in. What number of acres are represented? Ans. 371200A.

2. A merchant marks his goods with two prices, one for ready money, and the other for a credit of 6 mo. What ratio ought the two prices to bear to each other, allowing 6% per annum simple interest? Ans. 100 to 103.

3. A grocer buys two kinds of tea, one at $.80, and the other at $.50 a pound, and mixes them in the proportion of 5 parts of the cheaper to 7 parts of the dearer. At what price per pound must he sell the mixture, so as to realize 25% profit on the cost? Ans. $.8433.

4. A circular plot of ground containing an acre has a walk all around it on the inside, 2 yards wide. Find the area of the space within the walk. Ans. 68.849 P.

5. A butcher paid $152 for calves and sheep, paying $6 apiece for the calves, and $4 a head for the sheep; he sold of his calves and of his sheep for $46, and in so doing lost 8% on their cost. How many of each did he purchase? Ans. 12 calves; 20 sheep.

6. I borrowed a sum of money at 6% annual interest, and loaned it at 8% interest semi-annual, receiving compound interest for the second half-year, and gained thereby at the end of the year $860. What was the sum borrowed? Ans. $39814.81.

7. If a reservoir 24 ft. 8 in. long by 12 ft. 9 in. wide is full of water, how many cubic feet must be drawn off to lower the surface 9 in.? Ans. 2353 cu. ft. S. The sales of a publisher amount to $250000. Onefourth of the sales are made at a profit of 33%, threefifths at a profit of 20%, and the remainder at a loss of 25%. Find the cost of the stock sold. Ans. $214438.88.

9. If a cannon-ball 8 inches in diameter weighs 128 lb., what will be the weight of a similar ball 15 inches in diameter? Ans. 843 lb.

10. Smith owed Jones $1800, due July 18; he paid $560 before, and the remainder after the whole was due. When were the payments made, if they were 45 days apart? Ans. June 17 and Aug. 1.

11. The triangular gable of a certain building has a base of 45 feet, and the perpendicular height is 16 ft. What will the lumber cost required to cover both gables, at $1.87 per hundred feet, board measure? Ans. $13.50.

12. The first of 6 boys can run 3 rods as soon as the second can run 2 rods; the second 5, as soon as the third 6; the third 7, as soon as the fourth 8; the fourth 9, as soon as the fifth 10; and the fifth 15, as soon as the sixth 14. How many rods will the sixth run while the first is running 135 rods? Ans. 128 rods.

13. A walk 12 feet wide surrounds a square garden. The area of the walk being an acre, what is the area of the inclosed square? Ans. 4 A. 76.6 P.

14. What sum must a man save annually, commencing at 21 years of age, to be worth $40000 when he is 50 years old, his savings being invested at 6% compound interest?

Ans. $543.18.

15. A bin 9 ft. 6 in. long, 6 ft. wide, and 4 ft. 3 in. deep, is full of wheat. What is its value at $2.05 a bu.? Ans. $339.05.

16. There is a room whose length, breadth, and height are as the numbers 3, 2, 1, containing 4374 cu. ft. What are its dimensions, and what is the distance of its remotest corners? Ans. 27, 18, 9, and 33.67 ft.+. 17. If I buy 120 shares of stock at 74, 150 shares at 68, and 130 at 54, how many shares must I buy at 40, so that I may sell the whole at 60, and gain 20%? Ans. 606.

18. A wholesale dealer sells to a retailer at 10% profit, and the retailer sells to the consumer at 50% profit; what part of the price paid by the consumer is profit? Ans. 1.

19. A man spent of all the money he had and $1 more; then of the remainder and $ more; then of the remainder and $ more, when he had $5 left. How much had he at first? Ans. $47.

20. Four men took a prize worth $6213, which they agree to divide in proportion to the following fractions: A, B, and C are to have ; B, C, and D, ; A, C, and D, ; and A, B, and D, 2. What does each receive?

Ans. A, $2130; B, $1635; C, $1308; D, $1090. 21. A man bought a farm for $10000, giving a 3 years' note, at 7% annual interest, and rents it at 10%, payable quarterly. He paid 2% annually, in advance, for repairs, and at the end of 2 yr. sold the same at 1% discount and took up his note. Reckoning 7% simple interest on all expenditures and income, did he make or lose by the transaction and how much? Ans. $131.50 gain.

22. How many square feet of tin will cover a hemispherical dome, whose diameter is 10 feet? Ans. 157.08 sq. ft.+.

23. What must be the length of a halter rope, one end fastened to a stake, that will allow a horse to graze on of an acre? Ans. 58.85 ft.

24. A man 34 years old insured his life for $6000, on the 10-payment plan. When he died, there was a net gain to his family of $4463.40. How many payments had

he made?

Ans. 5.

25. W. D. L. Robbins bought 50 shares of bank stock at 106. From the time of purchase until the end of 3 yr. 3 mo. he received a semi-annual dividend of 4%, when he sold the stock at 111. Money being worth 7% compound interest, what did he gain? Ans. $274.62.

26. A and B run a 100-rod race, and A wins by 2 rods ; C and D run over the same course, and C wins by 6 rods; B and D run over it, and B wins by 4 rods. If A and C run, which will win, and by how much? Ans. C, by .085 rd.

27. If 2 acres of grass, together with what grows on 2 A. while they are grazing, keep 8 cows 3 wk., and in like manner 5 A. keep 15 cows 6 wk., how many acres will be required to keep 15 cows 2 wk.? Ans. 3 A.

28. Two casks, each containing 8 gallons of wine, P and M, are mixed as follows: 1 gallon is taken out of each and put back into the other. This is repeated 4 times; how much of the original contents remains in each cask? Ans. 511 gal.

29. Which is the cheaper, a suit of clothes which costs $56 and will last 18 months, or a suit that costs $35 and will last 10 months; and how much will a man save in 20 years who wears the cheaper suit, interest not being reckoned? Ans. The $56 suit; $93 gain.

30. A resident at Rome, having a bequest of $12500 made him in New York, orders the remittance to be made to his agent in London, who remits the proceeds to Rome, reserving his commission of 1% on the draft sent. If the course of exchange on London is 4.901 in New York, and the rate between London and Rome is 25.8 lire to the pound sterling, how much does the man realize from his bequest? Ans. 65422.14 lire.

31. Three men can do a piece of work in 30 days, A and B each doing the same amount of work in the same time; if either A or B are absent, the two others can do of the work in 28 days. In what time can each separately do the work? Ans. A or B, 74, da.; C, 157 da.

32. The annual rent of a farm is $1200, payable in money, in wheat, and the balance in corn, the average prices being as follows; wheat $1.50, and corn $.65 a bu. What will be the rent when the average prices of wheat and corn are $1.75 and $.80 per bushel? Ans. $1365.38. A., how far is the

33. In a square lot containing 1 center from each corner, and from the middle of each side? Ans. 11.31 rd., and 8 rd. 34. A cistern has 3 pipes; the first can fill it in 3 hr., the second in 4 hr., and the third can empty it in 1 hr. If the cistern is full, and these three pipes be opened in order at 3, 4, and 5 o'clock, at what time will the cistern be emptied? Ans. 12 min. past 7.

35. The fore-wheel of a carriage, which is 7 feet in circumference, makes 792 more revolutions than the hindwheel in a distance of 3 miles. Find the circumference and the diameter of the hind-wheel.

Ans. Circum., 10 ft.; diam., 3.183 ft.+.