794. The sugar-beet yields 6% of its weight in sugar. One acre of land will produce 25,000 lbs. of beet-root, worth $2.75 per ton. How many acres of land are needed to supply with beet-root a sugar factory whose annual production of sugar is 100,000 lbs., and what is the value of the beet-root supplied?

795. Crystallized blue vitriol is composed of 63.3 parts, by weight, of copper, 32 parts of sulphur, 80 parts of oxygen, and 90 parts of water. Find its percentage composition. How much copper is there in 200 lbs. of blue vitriol?

796. Two coal-dealers in Pittsburg sold an equal amount of coal. One received from a Boston merchant $6200 on the delivery of the coal; the other took a note for $6800 for 2 yrs. 6 mos., without interest, from a New York banker. If money commands 7%, which dealer received the greater price for his coal?

797. $14,400 in 3% United States bonds at 101 are transferred into a 44% railway stock at 1251, the expenses of the operation amounting to $50.98. Find the alteration. in the income produced.

798. Find the net cash amount of a bill of $750, discounts being, 25, and 171⁄2, and an additional discount of 5% for cash.

799. A milkman gains $1401.60 in 1 yr. by selling milk at 8 cents per quart. He sells on an average 42 gals. daily. What is his rate of profit per cent?

800. A milkman gains $2102.40 in 1 yr. by selling milk at 8 cents per quart. He sells on an average 48 gals. of milk every day. What is his rate of profit per cent?

801. A man has a sum of money due him at the end of 4 yrs., simple interest being reckoned at 5%. What fraction of the sum could he take off for payment at once?

802. Three pipes carry water into a tank. The first running alone can fill it in 4 hrs., the second in 5 hrs., and the third in 6 hrs. How long will it take them to fill the tank if they run together?

803. A man has a bill for $1353.60 due him at the end of 4 yrs. Find what sum he could take for cash payment, simple interest being reckoned at 5%.

804. A vessel has a leak which admits 127 gals. of water in 3 min. The pumps are just able to remove 2094 gals. in 5 min. Can the pumps keep the amount of water in the vessel from increasing?

805. A good harness oil is composed of suet, lard, turpentine, beeswax, and the rest olive oil. Find the cost of 1 lb. of this oil, if the suet costs 12 cents per pound, the lard 19 cents, the beeswax 45 cents, the turpentine 16 cents, and the olive oil 28 cents.

806. Reduce 1184 to its lowest terms.

228462

807. If a loaf weighing 44 lbs. be sold for 6 cents when wheat is 72 cents per bushel, what should be the price of 150 lbs. of bread when 8 bu. of wheat bring $8.64?

808. One pipe can fill of a vessel in 1 hr. Another pipe can empty of it in 3 hrs. If the vessel be empty, and both pipes are opened, in what time will the vessel be full?

809. A clock which gains 7 min. in 24 hrs. is 12 min. fast at midnight on Sunday. What o'clock will it indicate at 4 o'clock on Wednesday afternoon?

810. At what point must the hands of a clock be placed at noon to indicate the true time at 7.30 P.M., if there be a daily gain of 3 min. ?

811. A reservoir 10 ft. deep contains water to the height of 2 ft. It is supplied with water by a pump which could fill it if empty in 5 hrs. The water is taken from the reservoir by another pump, which is capable of emptying it, when full, in 94 hrs. If both pumps are set in action, in what time will the reservoir be completely full of water?

812. A steam pump, employed to raise water to a reservoir, will fill the reservoir in 10 hrs. 25 min. when it works well. One day the efficiency of the pump was reduced by an accident, just as the reservoir was full. How long did it take the pump on this occasion to fill the reservoir ?

813. If $480 amounts to $648 in 10 yrs. at compound interest, what would $24,000 amount to in 20 yrs. at the same rate?

The first stone can

814. A grist mill has 3 mill-stones. grind 5 bu. of corn in 2 hrs., the second 10 bu. in 3 hrs., and the third 15 bu. in 4 hrs. How many bushels can all three grind in 1 hr.? How many hours will it take them to grind 460 bu.?

815. By selling out 3% bonds at 102, and investing the proceeds in a railway stock which pays an annual dividend of 7%, a man finds that he can double his income. What is the price of the stock?

816. A fountain can fill a fish basin in 24 hrs. Another fountain can fill it in 3 hrs. If the basin is dry, and both fountains are turned on, in what time will it be full? If the basin holds 15,000 gals., how many gallons will each fountain empty into it in 1 min.?

817. The weight of the water contained in a rectangular cistern 8 ft. long and 7 ft. wide is 934 cwt. of 112 lbs. each. What is the depth of water in the cistern if a cubic foot of water weigh 1000 oz.?

818. A ship 40 mi. from the shore springs aleak, which admits 3 t. of water in 12 min. 60 t. would suffice to sink her, but the ship's pumps can throw out 12 t. of water in an hour. Find the average rate of sailing, that she may reach the shore just as she begins to sink.

819. Two fountains empty into the same basin. The first can fill it in 3 hrs. and the second in 5 hrs. The first is allowed to play alone for 1 hr., and then the second for 1 hrs. Both fountains are then turned on. In what time will the basin be filled?

820. A certain district contains a rural population of 3789 and a town population of 2354. Among the rural population, the births are 31 per thousand annually, and the deaths 25 per thousand. Among the town population the births are 42 per thousand, and the deaths 30 per thousand. What is the annual increase or decrease of the whole population?

821. A dealer bought 2 horses giving as much for one as for the other. He sold the more expensive horse at a gain of 15%, and the other at a loss of 5%, receiving $715.20 for both horses. What did he pay for each horse?

822. In Fahrenheit's thermometer the freezing-point is marked 32°, the boiling-point 212°; in the Centigrade the same points are respectively 0° and 100°. Express 4° C. in Fahrenheit's scale, and 62° F. in the Centigrade scale.

823. A certain zinc ore yields 55% of metallic zinc, and a certain copper ore yields 25% of metallic copper. In making brass from these two metals 5% of the metal is wasted, and the coals and labor cost as much as the metal. The zinc ore is worth $43.20 per ton, delivered, and the copper ore $81.60. What is the net cost per ton of brass consisting of a mixture of equal parts of the two metals?

CHAPTER VI.

PROPORTION.

MISCELLANEOUS EXERCISES

(illustrating the applications of the Rule of Three).

1. Find a fourth proportional to 3, 15, 7.

2. Find a number which has the same ratio to 21 that 45 has to 9.

3. A's wealth is to that of B as 3 to 7. B is worth $63,000. What is A worth?

4. In five years the population of a mining town increased from 200 to 16,000. If the rate of increase remain the same, what will the population be after five years more?

5. If 75 men can do a piece of work in 12 dys., how many men could do it in 20 dys.?

6. What must be paid for 12 lbs. of indigo, when 7 lbs. cost $12.75?

7. If twelve men reap a field in 4 dys., what time would be required for 32 men to reap it?

8. A ship performs a voyage in 63 dys., sailing at the rate of 6 knots an hour. How long would it take her if she sailed 7 knots an hour?

9. A milkman having failed, settled his accounts, and found he had property to the amount of $215, while he owed $1075. If his creditors demand immediate payment, how much will they receive on a dollar?