26. A box, 4 ft. 8 in. long and 4 ft. wide, holds 128 gallons; how many bushels would it hold if it were 5 inches deeper?

27. How may 140 bricks be put in a box whose inside dimensions are 32, 14, and 20 inches?

28. A farmer has a section of land, and after reserving the S. E. quarter for himself, desires to divide the remaining 3 quarters equally among his 4 sons, so that each of the 4 parts shall have the same shape. Required the shape, amount and description of each son's part?

29. A garden is 12 ch. long and 5 ch. wide; how many acres larger would it be if it were 3 ch. longer and 1 ch. wider?

30. A rectangular field is 72 rd. long and contains 18 acres; if its width were 24 rd. greater, how much greate must its length be that its area may be doubled?

31. A pile of bricks is 3 ft. long, 2 ft. wide and 1 ft. high; how many more bricks are required to make the pile 1 ft. longer, 1 ft. wider and 1 ft. higher?

32. Around a garden 18 rd. long by 10 rd. wide is a ditch 2 ft. wide and 3 ft. deep. This ditch being insufficient it was cut 1 ft. 6 in. wider from the outer edge, and the whole ditch 1 ft. deeper, how many cu. ft. of dirt were thrown out in making this change?

QUESTIONS.

What is mensuration? A plane figure? Area? Rectangle? How find the area of rectangular surfaces?

What is said about shingling? Carpeting? Plastering, etc.? Dividing and designating land? Draw and number the sections of a township.

What is a rectangular solid? Contents or volume? How find the volume of a rectangular solid?

What is said about bricks? Capacity of tanks? Of bins? Board 'measure?

CHAPTER IV.

PERCENTAGE.

321. A per cent is a number of hundredths.

(1) 5 hundredths, 1 and .063 are per cents.

Per cent is a contraction of per centum, which means by the hundred. Thus, when we say that 7 per cent of a number of apples are rotten, we mean 7 of every 100 are decayed.

322. The sign of per cent is %.

(1) 7 per cent, 1, .07 and 7% all have the same meaning.

Oral Exercises.

Reduce 60 per cent to an equivalent common fraction.

(19) Reduce & to a per cent.

Solution: The process is the same as that of reducing to a frac

tion whose denominator is 100, Art. 158. It may be reduced thus:

since 100%

of 100% = 371⁄2%.

Reduce the following to equivalent

per cents:

し

20. 25. 3.

27. .

28. .

40. What part of a number is 5% of it? 25% of it? 50%? 75%? 12% 33%? 100%?

41. What per cent of a number is of it? of it??o? 2?? All of it?

42. What is the value of 5 per cent + 8 per cent? 9% +8%? 16% -7%? 12% +15% - 20%? 1 - 60% ? 43. A boy spent 75% of his money for apples; how much of it had he left?

44. A lad gave 60% of his money for a saddle and 25% of it for a bridle; how much had he left? How much more did the saddle cost than the bridle?

45. How much is of 38%

of 40%? of 56%? 25%

of 80%? 333% of 24%? 12% of 32%?

323. Percentage is the process of computing by per

cents.

In this process there are primarily three elements, viz.: the base, the rate, and the percentage.

324. The base is the number of which the per cent is taken; the rate is the given per cent; and the percentage is the result of taking that part of the base expressed by the

rate.

Illustration.-20% of $35

=

$35.20 = $7.

Here, $35 is the base, 20% is the rate, and $7 is the percentage. PRINCIPLE.-The base, rate, and percentage sustain to each other the relation of multiplicand, multiplier, and product.

Hence, when either two of the element

be found.

e third may

325. Base and rate given, to find the percentage.

(1) What is 40% of $180?

Solution: 40% of a number is 100% or 2 of the number; ¦ of $180 is $36, and is 2 times $36, = $72, Ans.

PRINCIPLE.--The percentage of any number is the same part of the base that the given rate is of 100%.

2. What is 20% of $35? 25% of $32?

25% of $32?

121% of $24? 331% of 48 days? 75% of 60 sheep? 60% of 350 men?

When the given rate is not a simple part of 100%, it is better to proceed as in the solution of the next problem.

(3) In a box are 160 pears, of which 7 per cent are rotten; how many of the pears are rotten?

Explanation.-Since 7% of a number is .07 of that number, I multiply the base, 160 pears, by the rate, expressed decimally, .07, and obtain the percentage, 12 pears.

Formula.-Percentage

RULE.-Multiply the base by the rate.

EXERCISE LXIII.

4. Find 6% of 50.
6. Find 4% of 325.
8. Find 20% of 635.
10. Find 25% of 60%.
12. Find 12% of 18.
14. Find 81% of $384.

5. Find 7% of $3875. 7. Find 16% of 2275 sheep. 9. Find 15% of 576 days. 11. Find 163% of 81%. 13. Find 17% of 35.

15. Find 391% of $1867.25.

16. A farmer had 575 sheep, of which he soid 4 per cent; how many did he sell?

17. I rented a house worth $1825 and paid 7% of its value for the use of it; what was the rent?

18. A merchant borrowed $900 and paid 163% for the use of it; what did the use of it cost him?

19. A cotton buyer invested $4275 in cotton, and sold it at a profit of 12%; how much did he gain?

20. Find 10% of 40% of $625.

21. Find 60% of 40% of 75% of $43.40.

22. A man owning 75% of a ship, sold 331% of his share; what part of the ship did he sell?

23. A father owned 65% of an estate, of which he gave his son 16%; what part of the estate did the son receive?

24. At a school of 150 pupils the average daily attendance is 90% of the whole number; what is the daily attendance?

25. A merchant collected $15675 and deposited 35% of it in bank; how much did he deposit?

26. What is the value of 70% of 60 oranges, at 5 cts. apiece?

27. If a man ride 163% of 1896 rods in 1 hour, how far will he ride in 175 hours?

28. From a cask of 40 gal. of oil, 15% leaked out; how much oil leaked out?

29. A man owes $65375, and is able to pay only 68% of his debts; how much money has he?

30. A farmer cultivated 240 acres of land, of which he planted 33% in corn, 25% in cotton, 20% in oats, and the balance in wheat; how many acres did he plant in each?

31. A has an income of $1280 a year; he pays 241% of it for board, 11% for clothing, % for servant's hire, and 153% for other expenses; how much does he pay for each item, and how much does he save?

32. A good cotton seed meal shows on analysis 3.3% phosphoric acid, 7.3% nitrogen and 1.7% potash; how much of each of these ingredients is contained in 1560 pounds of the meal?