The Complete Arithmetic

8. A man constructed a

cistern to hold 32 hhd., the

bottom being 6 ft. by 8 ft.

What was its depth?

9. How many more cubic inches in 189.5 gallons dry measure than in 189.5 gallons liquid measure?

10. Find the number of gallons in a cubic foot, correct to 4 decimal places.

11. A tank in the attic of a house is 6 ft. 6 in. long, 4 ft. wide, and 3 ft. 6 in. deep. How many gallons of water will it hold, and what will be its weight?

12. If 64 quarts of water are put into a vessel that will exactly hold 64 quarts of wheat, how much will the vessel lack of being full?

13. If a man buy 10 bu. of chestnuts at $5 a bushel, dry measure, and sell the same at 25 cents a quart, liquid measure, how much does he gain?

14. A cistern 5 ft. by 4 ft. by 3 ft. is full of water. If it is emptied by a pipe in 1 hr. 30 min., how many gallons are discharged through the pipe in a minute?

15. A vat that will hold 5000 gallons of water will hold how many bushels of corn?

16. A tank is 7 ft. deep, 4 yd. long, and 3 yd. broad. What weight of water is in it when just half-full?

17. A cellar 40 ft. long, 20 ft. wide, and 8 ft. deep is half-full of water. What will be the cost of pumping it out, at 6 cents a hogshead?

18. A reservoir 24 ft. 8 in. long by 12 ft. 9 in. wide is full of water. How many cubic feet must be drawn of to sink the surface 1 foot? How many gallons?

19. How many imperial gallons will a cistern contain that is 7 ft. 3 in. long, 3 ft. 8 in. deep, and 2 ft. 10 in. wide?

491. The Avoirdupois Pound contains 7000 Troy grains; hence the Troy pound is 4388 = 144 of an Avoir. pound; but the Troy ounce contains 1§o = 480 grains, and the Avoir. ounce, 10 = 437.5 grains.

The pound, ounce, and grain of Apothecaries' Weight are the same as those of Troy Weight, the ounce being differently divided.

WRITTEN EXERCISES.

493. 1. Change 10 lb. 8 oz. Avoir. weight to Troy.

OPERATION.-10 lb. 8 oz. = 168 oz.; 168 oz. × 437.5 =

and 73500 gr. ÷ 480 153 oz. 12 lb. 9 oz. Troy.

73500 gr.;

2. Change 15 lb. 10 oz. 12 pwt. Troy to Avoirdupois. OPERATION.-15 lb. 10 oz. 12 pwt. 190.6 oz.; 190.6 oz. × 480 = 91488 gr.; and 91488 gr. ÷ 437.5 = 20919 oz = 13 lb. 10 oz.

3. Find the value in Troy weight, of 9 lb. 10 oz. Avoir. 4. What is the value in Avoirdupois weight, of 16 lb. 8 oz. 10 pwt. 12 gr. Troy?

5. What is the value of a coffee urn, weighing 2 lb. 14 oz. Avoir., at $1.80 per ounce Troy?

6. How many ounces of gold are equal in weight to 6 lb. of lead?

7. If 8 lb. Avoir. of drugs are bought for $12 a pound, and retailed at the rate of $16.25 a pound, Apothecaries' weight, what is the gain on the whole?

8. What is the difference in the weight of 42 lb. of iron and 42.375 lb. of gold?

PERCENTAGE

ORAL EXERCISES.

495. 1. What is of $100? ? ? 75 ?

2. What is

3. What is

of $500? Of $700?

Of $1000 ? of $600? o? 200? 130%? 4. How many hundredths of $100 are $5 ? $7? $18? 5. How many hundredths of $500 are $25? $35? $50? 6. How many hundredths of any number is of it? ? 496. Percentage is a term applied to computations in which 100 is employed as a fixed measure, or standard.

The term percentage is also used to denote the result found by applying that standard to any given number.

497. Per Cent. is an abbreviation of the Latin phrase per centum, which signifies by the hundred.

Thus,5 per cent. means 5 of every 100, or 15, the five standing for the numerator, and the words "per cent." for the denominator 100. The phrase per cent.," wherever it occurs, should invariably suggest to the mind a decimal to the hundredths place. Thus, 25 per cent. =

for .25.

100

498. The Sign of Per Cent. is %. It is read per cent. Thus 6% is read 6 per cent.

6 per cent., 6%, 18, and .06 are equivalent expressions; the first two are used in the statement of questions, the other two in performing the operations.

7. How many hundredths of a number is 7% of it? 9%? 31%? 15%? 83%? 63%? 25%? 184%? 45% ?

8. What per cent. of a number is 1 of it? 1bo? .08?

.12? ? ? .025? .00 .04? .375? .0325?

100

499. What per cent. of a number is of it?

ANALYSIS. Since the whole of any