12. How long a time will be required for one of the heavenly bodies to move through a quadrant of a circle, if it moves at the rate of 1' 3" per minute?

13. The distance from Eastport, Maine, to San Francisco, California, is about 2760 miles. If a man, starting from Eastport, travel toward San Francisco for 75 days, at the rate of 24m. 3fur. 20rd. per day, how far will he then be from San Francisco?

14. A certain island is 75 miles in circumference. A and B, starting at the same time, and from the same point, and going in the same direction, travel round this island, A at the rate of 24m. 3fur. 10rd., and B at the rate of 15m. 6fur. 20rd. per day ; how far apart are A and B at the end of five days?

15. A merchant bought 125 barrels of flour, at 1£ 15s. 6d. per barrel, and afterward exchanged the flour for 260 yards of broadcloth, which he sold at 18s. 9d. 3qr. per yard; did he gain or lose, and how much?

16. How many feet of boards will be required to make 12 boxes whose interior dimensions are 5ft. 6', 4ft. 9′, and 3ft. 8', the boards being 1' in thickness?

17. How many feet less are required to make 12 boxes whose exterior dimensions are like the interior of those in Ex. 16, the boards being of the same thickness? Ans. 111ft. 4'.

18. What is the difference of the capacities of the two sets of boxes described in Ex. 16 and 17? Ans. 122ft. 10'.

19. How many times will a wheel 9ft. 8in. in circumference turn round in running from Boston to Worcester, a distance of 44m. 4fur.?

20. How many gallons, wine measure, in a water tank 4ft. Gin. long, 3ft. 8in. wide, and 3ft. 9in. deep?

21. If a teacher devote 5h. 30m. per day to 50 pupils, what is the average time for each pupil?

22. If a man, employed in counting money from a heap, count 75 silver dollars each minute, and continue at the work 12 hours each day, in how many days will he count a million of dollars?

23. How many pounds of iron in one scale of a balance, will poise 75 pounds of gold in the other scale?

PERCENTAGE.

221. PER CENT. is a contraction of per centum, a Latin phrase which means by the hundred; thus, ten per cent. of a bushel of corn means ten one-hundredths of it; i. e. ten parts out of every hundred parts; six per cent. of a sum of money, is six one-hundredths of the sum, i. e. $6 out of every $100; etc. NOTE. Instead of the words per cent., it is customary to use this sign, %; thus, 6 per cent. is written 6%; 4 per cent., 4%.

222. The RATE PER CENT. is the number for each hundred ; thus, 6% is 18,or .06, i. e. 6 parts for each hundred parts.

223. The PERCENTAGE is the sum computed on the given number; thus, the percentage on $200 at 6 per cent. is $12.

224. The BASE of percentage is the number on which the percentage is computed; thus, $200 is the base on which the percentage is computed in Art. 223; a bushel of corn is the first base mentioned in Art. 221.

225. The rate per cent., being a certain number of hundredths, may be expressed either decimally, or by a common fraction, as in the following

NOTE. When the per cent. is expressed by a decimal of more than 2 places, the figures after the second decimal place must be regarded as parts of 1 per cent.; thus, (in the last line of the foregoing table,) .125 is 12 or 12 per cent.

Ex. 1. Write the decimal for 4 per cent.

Ans. .04.

2. Write the decimal for 8 per cent.; 12 per cent.; 16 per cent.; 25 per cent.; 72 per cent. .

3. Write the common fraction for 163 per cent. ; 20 per cent. ; 33 per cent.; 75 per cent. 1st Ans.

PROBLEM 1.

226. To find the percentage, the base and rate per cent. being given.

Ex. 1. B had $175, but lost 8 per cent. of it; how many dollars did he lose?

$175
.08

$14.00, Ans.

Since 8 per cent. is .08 2, the loss is found by multiplying $175 by .08 or by

Hence,

RULE 1. Multiply the base by the per cent., written decimally; or,

RULE 2. Find such part of the base as the rate is of 100 (Art. 151).

2. A farmer having 48 sheep, lost 25 per cent. of them; how many did he lose?

221. Meaning of per cent.?

.25

= 1.

4 of 4812, Ans.

Or, 48 × = 12, Ans.

222. Rate per cent.? 223. Percentage? 224. Base of percentage? 225. In what ways may the rate be expressed? If expressed decimally by more than two figures, what are the figures after the second decimal place? 226. Rule for finding percentage when the base and rate are given? Second Rule?

3. What is 6 per cent. of $250 ?
4. What is 8 per cent. of $250?

5. What is 12 per cent. of $500 ?

Ans. $15.

Ans. $62.50.

6. What is 83 per cent. of 600bush. of wheat?

Ans. 50bush.

7. What is 163 per cent. of 1200 lb. of cheese?

Ans. 200lb.

8. A farmer cultivates 25 acres of corn this year, and intends to cultivate 20 per cent. more next year; how many acres does he intend to cultivate next year ? Ans. 30.

9. In an orchard of 900 trees, 333 per cent. are peach trees; how many peach trees are there in the orchard?

10. A teacher pronounced 56 words for his pupils to spell, but 144 per cent. were mis-spelled; how many words were misspelled?

11. Only 663 per cent. of a class of 27 pupils solved a problem given them for a lesson; how many of the class failed?

12. The population of a certain city is 18775, what will it be in one year from this time if it gains 8 per cent.?

13. The population of a certain State is 1376875, what will it be in one year if it loses 12 per cent.?

14. A and B commenced business, each with $8456. A gained 25 per cent. and B lost 12 per cent.; how much was A then worth more than B?

15. A speculator paid $56895 for a lot of flour, and lost 9 per cent.; for what sum did he sell the flour?

16. One acre of corn yields 80 bushels, and another acre 20 per cent. more; how many bushels does the second acre yield?

PROBLEM 2.

227. To find the rate per cent. when the base and percentage are given.

Ex. 1. One dollar is what per cent. of $4?

4) 100

25, Ans.

reduced

One dollar is of $4, and to a decimal is .25; i. e. $1 is 25 per cent of $4. The same result is obtained by multiplying $1 by 100, and dividing the product by 4. Hence,

te and base. the per

RULE. Multiply the percentage by 100, and divide the product by the base.

=

NOTE. This rule is the converse of that in Art. 226; thus, 25 per cent. of $4 is $4 X .25 $1; and, conversely, $1.00 - $4 = .25, i. e. 25 per cent. 2. What per cent. of $150 is $18?

1800÷150=12 per cent., Ans.
Ans. 63 per cent.

3. What per cent. of $300 is $19?
4. What per cent. of $350 is $43.75?

Ans. 12 per cent.

Ans.

5. What per cent. of $340 is $34? 6. What per cent. of $64 is $16? 7. What per cent. of $1000 is $5? of 1 per cent. 8. B inherited $3500, and in 6 months spent $875; what per cent. of his inheritance did he spend? What per cent. had he remaining? Ans. Spent 25 per cent., and had 75 per cent.

9. Out of a cask of wine containing 96 gallons, 32 gallons were drawn; what per cent. of the whole remained in the cask?

10. A merchant having $1000, deposited $650 in a bank; what per cent. of his money did he deposit?

11. A teacher having a salary of $2400, spends $2000 annually; what per cent. of his salary does he save?

PROBLEM 3.

228. To find the base when the percentage and the rate are given.

Ex. 1. $6 is 3 per cent. of what sum ?

If $6 is 3 per cent., then 1 per cent. is of $6, which is $2, and if $2 is 1 per cent., then 100 per cent. is 100 times $2, which is $200; .. $6 is 3 per cent. of $200, Ans.

The same result is obtained by first multiplying $6 by 100, and then dividing the product by 3; thus, $6003 $200, Ans. Hence,

RULE. Multiply the percentage by 100, and divide the product by the rate.

227. Rule for finding the rate when the base and percentage are known? What of this rule, and that in Art. 226? 228. Rule for finding the base when the percentage and rate are known?

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