The ratio of two similar solids is equal to the cube of the ratio of their like dimensions; and,

The ratio of the like dimensions of similar solids is equal to the cube root of the ratio of their volumes.

I. There are two rectangular gardens similar in shape. If the first is five rods long, and the second 20 rods, how many times as large as the first is the second? Solution: The ratio of 20 to 5 is 4, 42: 16. Answer:

16 times as large.

2. How many pipes 2 inches in diameter will discharge as much water as one pipe 6 inches in diameter?

3. The area of a triangular lot whose base is 120 ft., is 900 sq. yd. What is the base of a similar lot whose area is 3600 sq. yd.?

4.

A rectangular field is 50 rods long, and 32 rods wide. What are the dimensions of a similar field whose area is 90 acres?

5. A cistern whose capacity is 3200 gal. is filled by a 3-inch pipe in 80 minutes. In what time could a 4-inch pipe fill it?

6. If an iron ball 3 inches in diameter weigh 5 pounds, what would another ball of the same kind of metal weigh, whose diameter is 9 inches?

Solution: The ratio of 9 to 3=3. 33 = 27. 27X5 lb. 135 lb. Answer:

135 lb.

7. A log 10 ft. long contains 24 cu. ft. What would be the solid contents of a similar log 20 feet in length?

8. A pile of cracked stone 161 ft. long, 1 ft. wide, and 1 ft. high=I perch. What are the dimensions of a similar pile containing 64 perches?

9. How many marbles inch in diameter would be equal in volume to a marble ball 10 inches in diameter?

IO. A pyramid is 5 ft. square at the base, 7 ft. high, and its solidity is 62 cubic ft. What are the dimensions of a similar pyramid whose solidity is 500 cubic ft.?

Section VIII.

MISCELLANEOUS QUESTIONS.

I. The contents of a rectangular bin are 240 cubic feet. If its length, breadth, and depth inside have the ratios of 5, 3, and 2 respectively, what are its dimensions? For how much should a package of sugar weighlb. be sold to gain 25%, when sugar costs 10 ct.

2.

ing 7

a lb. ?

3. Bought a number of eggs at 1 ct. each, and twice as many at 13 ct. each. Sold all at the rate of 3 for 7 ct. What percent did I gain?

4. B has 50 acres of land, which is 66% of A's. If each sell 48% of his land to the other, which will have the more, and how much more?

5. A lady has two watches, and a chain worth $20. The first watch and the chain are together worth as much as the second watch, but the second watch and the chain are worth 1 times as much as the first watch. What is the value of each watch?

6. A had 2 times as much money as B, but after A had borrowed 25 cents, and B had spent 10 cents, A had 3 times as much as B. How much had each at first?

7. of the square of a number-9= the square of of the same number + II. What is the number?

8. A drover spent $50 for sheep, and of the remainder of his money for cows, and found that he had of all his money remaining. How much had he at first?

9. The square of the cube root of a common fraction is ; what is the cube root of the square root of the same fraction?

ΙΟ.

A can mow a field in 8 da. B can mow of the field in of that time. In what time can both mow it?

II. On counting their money, it was found that B's money was of A's, and that C had as much as both of the others. If C had $5 more than A, how much had B?

12. A and B have equal incomes. A contracts an annual debt equal to of his income, while B lives upon

of his, and at the end of 8 yr. lends A enough to pay his debts, and has $320 left. What is the income of each? 13. If 77 lb. of sea-water contain 2 lb. of salt, how much salt must be added to make 52 lb. of the mixture contain 2 lb. of salt?

14. Io men were employed to do a piece of work, but 4 of them not coming, the others were occupied 3 days longer. In what time could 9 men have done the work?

15. What principal will in 3 yr. 4 mo., at 71%, amount to the same as $500 will in 4 yr., at 5% ?

16. Two men travel toward each other, one at the rate of 3 mi. per hour, the other 40% faster. If the distance was 60 mi., in what time did they meet, and how much farther did one travel than the other?

17. A dealer bought a number of horses for $1500. 6 having been stolen, he sold of the remainder at cost, and received $750. How many did he buy?

18. A man and his son can do a piece of work in 5 hr. If the son rests 24 hr. it takes them 6 hr. In what time can each do the work?

19. If a man loses $10 on a watch that he sells for $59, what % does he lose?

20. A boat, whose rate of sailing is 8 mi. per hr., makes a trip down a river whose current is 2 mi. an hr. How far can it go and return in 12 hr.?

21. A bought 6 peaches, B 8, and C 10. They were joined by D, and each ate an equal number. When D left, he gave the others 15 cents. How should they have

divided it?

22. of 224 is of the difference between two numbers, and the less equals of the greater. What are the numbers?

23. The sum of two numbers is 135, and their difference is of the smaller number. What are the numbers?

24. A pier was under water. The water rose 15 ft., and then there was as much of it under water as had been above water. How high was the pier ?

25. The amount of a certain principal for 3 yr. 6 mo. at a certain rate % is $484, and for 2 yr. 3 mo. at the same rate is $454. What are the principal and the rate? 26. An express train was to run 320 mi. at the rate of 40 mi. an hour, but after going of the distance, an accident delayed it 45 min. If it completed the trip at the rate of 45 mi. an hour, how much behind time did it arrive?

27. A and B entered into partnership for one year. A at first put in $500, and at the end of 4 mo. $500 more. B at first put in $1000, but at the end of 8 mo. drew out $500. They gained $500. How was it divided?

28. Sold molasses at 45 ct. a gal. and gained 12%. Had I bought it for 20% less, and sold it at 48 ct. a gal., what % would my profit have been?

29. A farmer plows an acre of ground for every 5 cows that he owns, and allows 1 acre of pasturage for every 3 cows. How many cows can he keep on 24 acres?

30. 20 men charter a pleasure-boat, but being joined

by 5 more, the expense to each is 50 ct. less. What do they pay for the boat?

31. B has 3 times as much money as A, but if A had $10 more, and B $20 less, A's money would equal B's.

How much has each?

of

32. A dairyman bought a number of cows for $750. Had he bought 10 more at $5 apiece less, all would have cost $1000. How many did he buy?

33. A steamer goes down stream at the rate of 10 mi. an hr., and up stream at the rate of 6 mi. an hr. If it takes 4 hr. less to go down than to return, how far did it go down?

34.

The wages of 6 men and 4 boys for one week is $90, and of 4 men and 6 boys is $75. How much do one man and one boy earn weekly?

35. A gamester won $750. He then lost of all his money, and found that he had twice as much as at first. What had he at first?

36.

The interest of A's money + of the interest of B's, for 3 yr., at 4% $180. How much has each, if of B's

37.

of A's?

=

of the difference in the contents of two cisterns is 112 gal., and the contents of the smaller are to those of the larger as 3 to 4. How many gallons are in each? 38. If 8 men can mow 100 acres of meadow in 5 da., in what time can 75 acres be mown if 3 of the men leave when the work is completed?

39. The square root of a certain number, divided by the cube root of the same number 3. What is the number?

40. If 40 lb. of sea-water contain 1 lb. of salt, how much fresh water must be added to make 10 lb. of the mixture contain lb. of salt?

41. A rectangular piece of marble is 5 in. square