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SECTION XI.

APPLICATIONS OF FOREGOING PRINCIPLES.

153. Introductory Note.

In performing the examples of this section, as of every other, the student should observe that the solutions and models of writing the work are designed to suggest methods of applying principles, and are not to be regarded as forms which must be rigidly followed. They should be deviated from when better forms can be discovered, or will apply. Indeed, a habit of examining each question carefully before attempting its numerical solution is one of the most valuable a pupil can acquire. A distinguished teacher once said, “ If I were required, on peril of my life, to perform a complicated problem in two minutes, I would spend the first minute in considering how to do it.”

151. Viscellaneous Problems. 1. How much will 75 yards of silk cost at $l; per yard ?

2. If it yards of silk cost $14, how much will 1 yard cost?

3. How many yards of silk, at $1$ per yard, can be bought for $14?

4. How much will a lot of land 28 rods long and 231 rods wide cost, at $225 per acre ?

5. How many pounds of coffee, at 154 cents per lb., can be bought for $8.40 ?

6. How many square feet and inches are there in a board 134 feet long and 2 feet wide ?

7. How many square feet in the four walls of a room, 151 feet long, 12 feet wide, and 84 feet high?

8. I bought a cask, containing 94 gallons of oil, at $1.375 per gallon; of it leaked out, and I sold the remainder at $1.50 per gallon. How much did I lose by the transaction ?

9. Mr. Whitney is worth $1473.21 more than Mr. Whipple, and Mr. Whipple is worth just as much as Mr. Whitney. How many dollars is each of them worth?

Suggestion. — If Mr. Whipple is worth only t as much as Mr. Whitney, the difference between the values of their estates must equal of Mr. Whitney's estate.

5

3; 23 3 10. What is the value of of

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12. If 84 yards of broadcloth cost $293, how much will 104 yards cost ?

13. If 81 yards of broadcloth can be purchased for $299, how many yards can be purchased for $35/?

14. If 10} yards of broadcloth cost $351, how much will 8 yards cost ?

15. If $354 are paid for 10} yards of broadcloth, for how many yards should $293 be paid ?

16. If it of a ton of hay costs $17.50, how much will two loads cost, one weighing of a ton, and the other di of a ton ?

17. If 22 horses eat 414 bushels of grain in 102 days, how many

bushels will 21 horses eat in 91 days ? Solution. As the answer is to be in bushels of grain, we write 411, or 103, as the number to be operated on. If 22 horses eat 165 bushels, 1 horse will eat 22 as much in the same time, which may be expressed

165 by making 22 a factor of the denominator ; thus,

If i horse

4 X 22 will eat this quantity in 101, or 24, days, in 1 day he will eat at of this, and in 2 half-days, or a day, he will eat twice this result, expressed by making 21 a factor of the denominator, and 2 a factor of the numcra

165 X 2 tor; thus,

* If i horse eats this quantity, 21 horses 4 X 22 X 21 will in the same time eat 21 times this, expressed by making 21 a factor

165 X 2 X 21 of the numerator ; thus,

it If 21 horses eat so much in

4 X 22 X 21 1 day, in 9}, or 48, days, they will eat 48 of this, which may be expressed by making 28 a factor of the numerator, and 3 a factor of the

165 X 2 X 21 X 28 denominator ; thus,

I 4 X 22 X 21 X 3 Hence the written work and answer are as follows:

5 15

7 165 x 2 x 21 x 28 bu.

= 35 bu 4 x 22 x 21 x 8

2 NOTE. - It will be seen that in the solution, each condition of the question was considered by itself, without reference to the other conditions, and that the problem was dealt with as though composed of the following series of simpler problems :

1. If 22 horses eat 41} bushels of grain in a giren time, how many bushels would i horse eat in the same time?

• This shows how many bushels 1 horse will eat in 1 day.
+ This shows how many bushels 21 horses will eat in 1 day.

This shows how many bushels 21 horses will eat in 9f days.

2. If i horse eats the quantity obtained as the answer to the last question in 10 days, how many bushels will he eat in 1 day?

3. If i horse eats so much (the answer last obtained) in a day, how many bushels will 21 horses eat in the same time?

4. If 21 horses eat so much (the answer last obtained) in 1 day, how many bushels will they eat in 9f days?

The student should notice that the question in each case has been, “How many bushels ?” and that the denomination of each answer has been the same as that required for the final answer.

18. If 22 horses can be kept 10 days on 411 bushels of grain, how many horses can be kept 9} days on 35 bushels of grain.

19. If 22 horses can be kept 101 days on 414 bushels of grain, how many days can 21 horses be kept on 35 bushels of grain ?

20. If 21 horses eat 35 bushels of grain in 9 } days, how many bushels will 22 horses eat in 104 days ?

21. If 21 horses can be kept 91 days on 35 bushels of grain, how many days can 22 horses be kept on 414 bushels of grain ?

22. If 21 horses can be kept 9 days on 35 bushels of grain, how many horses can be kept 104 days on 414 bushels of grain ?

23. If 7 men, by working 8 hours per day during 6 days of the week, can earn $320% in 51 weeks, how many dollars would 4 men earn in 44 weeks, by working 9} hours per day, and 5 days per week ?

24. If it costs $9.25 to dig a ditch 47 feet long, iş deer, and 3 feet wide, how much will it cost to dig a ditch 707. feet long, 2 feet deep, and 44 feet wide ?

25. If, when flour is $63 per barrel, a six-cent loaf weighs 15 OZ., how

many ounces ought a ten-cent loaf to weigh when flour is $9% per barrel ?

26. If a block of oak, 33 feet long, 1 foot wide, and of a foot thick, weighs 1204 lb., how much will a block of pine, 8 feet long, 2 feet wide, and is feet thick weigh, pine being only as heavy as oak?

27. If I men, by working 10 hours per day during 6 days

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