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6. How many pounds of sugar, at the rate of 8 pounds for a dollar, can be bought for $5.75 ?
7. If a man can earn $1 in of a day, how much can he earn in of a day?
8. If 23 acres of land cost $137.84, how much will 5 acres cost?
9. If 3 yards of cloth can be bought for $43, how many yards can be bought for $24?
10. How many bushels of grain at § of a dollar per bushel can be bought for $5?
11. I bought 8 barrels of apples for $15, and afterwards 12 barrels at the same rate. What did I pay for the last lot?
12. How many men will it take to perform a piece of work in 8 days which 12 men can perform in 6 days?
13. How many days will it take 50 men to do a piece of work which 80 men can do in 40 days?
14. If 9 men can build a wall in 2 weeks, how many men must be employed to build it in 6 weeks?
15. If a ship's crew of 20 men have provisions enough for 18 months, how many months will the provisions last if 10 men be added to the crew?
16. How many men must be employed to do a piece of work in of a month, which 36 men can do in 1 months?
17. If sugar is worth 12 cents per pound when weighed by the correct weight, how much is it worth per pound Troy?
18. How many yards of silk of a yard wide will it take to line 25 yards of broadcloth 13 yards wide?
19. If George does as much work in 9 days as Joseph does in 8, in how many days will George do as much work as Joseph does in 9 days?
20. If Henry does as much work in 7 days as William does in 11, how many days will it take William to do as much work as Henry does in 7 days?
21. If 18 bags of coffee each weighing 96 pounds can be bought for $288, how many bags each weighing 75 pounds can be bought for the same sum?
22. I bought 2 pieces of cloth for the same sum per piece, but the first piece cost 1 times as much per yard as the second. If the second piece contained 25 yards, how many yards did the first piece contain?
23. I own two equal lots of land, but the length of the first lot is only that of the second. Now, allowing that the second lot is 35 rods wide, how wide is the first lot?
106. Problems in Compound Proportion.
(a.) In solving problems in Compound Proportion, the third term is determined as in Simple Proportion. Then, taking any two similar conditions, we determine what ratio an answer depending on them alone would have to the third term, and, after writing this ratio, consider what ratio an answer depending on any two other conditions which are similar to each other would bear to this, and so proceed till all the conditions are considered. Solving the resulting proportion will give the result sought.
1. If 9 men can mow a field containing 6 acres in 3 hours, how many hours will it take 12 men to mow a field containing 8
SOLUTION.-3 hours will be the third term, for the answer is to be in hours. As it takes 9 men so many hours, it will take 12 men the same part of this that 9 is of 12, expressed by making 9 the second term, and 12 the first. As it takes so many hours to mow 63 acres, it will take the same part of this time to mow 8 acres that 8 is of 63, which may be expressed by making 8 a factor of the second term and 63 a factor of the first. We 12: 9 3 × 9 × 82 12 X 63 2D SOLUTION.-We write 3 hours for the third term. Then, as it will take 12 men a less number of hours to do a piece of work than it will take 9 men, we make 9 the second term and 12 the first. As it will take them longer to mow 84 acres than it will to mow 64 acres, we make 8 the second term and 63 the first. We thus have the same proportion and answer as before.
thus have the proportion,
2. If 6 men can earn $78.28 in 8 days, how much can 11 men earn in 18 days?
3. If 6 men can earn $73.28 in 8 days, in how many days will 11 men earn $302.28?
4. How many men will it take to earn $302.28 in 18 days, if it takes 6 men 8 days to earn $73.28?
5. How many men will it take to earn $73.28 in 8 days, if it takes 11 men 18 days to earn $302.28?
6. If 11 men earn $302.28 in 18 days, how many dollars will 6 men earn in 8 days?
7. If 11 men earn $302.28 in 18 days, in how many days will 6 men earn $73.28?
8. If 7 men earn $75.60 in 54 days, how many dollars will 8 men earn in 49 days?
9. If 54 yards of cloth 5 quarters wide will make 12 suits of clothes, how many yards 5 quarters wide will it take to make 18 suits?
10. If a block of wood 6 ft. long, 14 ft. wide, and 13 ft. thick, weighs 771 pounds, how much will a block of wood 8 ft. long, 18 ft. wide, and 1 ft. thick, weigh?
11. If 7 acres of land are worth $1913, how much are 5 acres worth, allowing that 24 acres of the first lot are equal in value to of an acre of the last?
12. If a trench 100 ft. long, 4 ft. wide, and 3 ft. deep, can be dug for $100, for how many dollars can a trench 150 ft. long, 3 ft. wide, and 2 ft. deep, be dug?
13. A ship's crew of 25 men have provisions enough to give each man 30 oz. per day for 48 days, how many days would it last if they should take on board 15 more men?
14. If 15 ounces of wool make 3 yards of cloth 1 yard wide, how many ounces will be required to make 10 yards 6 quarters wide?
15. If 200 tiles 9 inches long and 8 inches wide will pave my yard, how many tiles 1 ft. long and 10 inches wide will it take to pave it?
16. If 6 house-lots 84 ft, long and 72 ft. wide are given for 40 double-eagles, how many house-lots 96 ft. long and 78 ft. wide ought to be given for 4623 quarter-eagles?
17. If 8 men, by working 10 hours per day, 5 days per week, 4 weeks per month, and 11 months per year, can earn $8800 in 3 years, how many dollars can 9 men working 93 hours per day, 5 days per week, 3 weeks per month, and 11 months per year, earn in 21 years?
18. If 7.5 pieces of cloth each containing 30 yards .9 of a yard wide can be bought for $112.50, how many pieces each containing 32.5 yards 1.62 yards wide can be bought for $425 ?
19. If 3 men can pick the apples in an orchard of 24 trees in 17 days of 10 hours each, how many days of 93 hours each would it take 10 boys to pick the apples in an orchard of 54 trees, allowing that the apples on 5 trees in the second orchard can be gathered as easily as those on 3 of the first, that 6 men do as much work as 9 boys, and that the boys are idle of the time?
107. Preliminary Definitions.
(a.) If I use an article of value belonging to another, it is but right that I should pay him for the use of it.
ILLUSTRATION.-We pay rent for the use of a house or store.
(b.) Money paid for the use of money borrowed from others or due to them is called INTEREST.
(c.) The money used is called the PRINCIPAL.
(d.) The principal and interest added together form the AMOUNT.
ILLUSTRATION.—If I should pay $9 for the use of $150 for 6 months, $9 would be the interest, $150 would be the principal, and $150 + $9, or $159, would be the amount.
(e.) Interest is usually reckoned at a certain number of hundredths of the principal for each year it is used. This number of hundredths is called the RATE PER CENT, or simply the RATE.
ILLUSTRATION.—If a man pays a sum equal to .06 of the principal for each year that he uses it, the rate is 6 per cent.
NOTE. The term PER CENT means simply one-hundredths, and applies to other quantities as well as to dollars and cents.
(f.) In computing interest, it is customary in this country to regard each calendar month as 30 days. In England, however, the months are reckoned according to the number of days which they contain.
(g.) Interest may be either SIMPLE or COMPOUND.
(h.) It is SIMPLE when reckoned on the principal only.
(i.) It is COMPOUND when, at regular intervals, the interest is added to the principal, so as to form a new principal on which interest is to be reckoned as on the original principal.
108. Legal Rate.
(a.) In most countries, laws called Usury Laws have been passed, regulating in some way or other the rates of interest.
(b.) Usury Laws commonly embrace the following particulars
1st. They fix the rate which shall be paid when no special rate has been agreed upon by the parties. The rate thus fixed is called the LEGAL RATE.