80. How many gallons of molasses, at 35 cents a gallon, will pay for 70 pounds of butter at 30 cents a pound?

81. A man received 32 pounds of sugar in exchange for 20 pounds of butter at 16 cents a pound; what did the sugar cost him per pound?

82. A man bought 80 turkeys, at the rate of 4 for 3 dollars; he sold them at the rate of 20 for 11 dollars; did he make or lose, and how much?

83. A farmer bought 24 sheep for 60 dollars; at how much per head must he sell them in order to gain 12 dollars?

84. Five men bought a threshing machine for $150; they rented it 4 weeks at $10 a week, and then sold it for $100; did they make or lose, and what was each man's share?

85. 5 barrels of flour are worth $60; how many hundred weight of pork, at $18 a hundred, will 3 barrels buy?

86. 4 men agree to build a barn for $160; but when it was half built 2 of the men quit work, and the remainder completed the job; how much should each man receive?

ANAL. STEPS.—1. Find what each man should receive for building the first half.

2. Find what each man should receive for building the second half.

3. Find the entire amount each man should receive.

87. Four men agree to chop 25 cords of wood for $48, but when it was half done, three of the

men quit, leaving the remaining man to finish the work. How should the money be divided?

88. If 4 men can do a piece of work in 24 days, how soon can 12 men do it?

ANAL. STEPS.-1. Find how long it will take 1 man to perform it.

FORM.*-If 4 men require 24 days, 1 man will require 4 times 24 days, which are 96 days.

2. Find how long it will take 12 men.

If it take 1 man 96 days, it will take 12 men 1 twelfth of 96 days, which is 8 days.

89. If 6 men can build a wall in 18 days, how many men will be required to build it in 24 days?

90. If 2 men can construct an engine in 15 months, in what time could 30 men construct it?

91. How soon can 12 men earn as much money as 9 men can earn in 32 months?

92. If 2 men can build a vessel in 30 months, how soon can 3 men build it?"

93. If 9 men can plant 5 acres in 16 days, how soon can 1 man do the work?

94. How long will it take 8 men to do what 12 men can do in 6 days?

95. If 40 barrels of apples cost $320, what will 5 barrels cost?

*Those who prefer may use the following:

FORM.-One man requires to perform the work 4 times as many days as 4 men; 4 men require 24 days; therefore 1 man requires 4 times 24 days, which are 96 days.

2. Twelve men require one twelfth as many days to perform the work as 1 man; 1 man requires 96 days; therefore 12 men require one twelfth of 96 days, which is 8 days.

96. If a horse can trot 36 miles in 6 hours, how many miles can he trot in 281 hours?

97. How many pounds of veal can be bought for 96 cents, if 9 pounds cost 72 cents?

98. If 4 quarts of vinegar can be bought for 36 cents, how many quarts can be bought for 216 cents?

99. If 3 pounds of cheese cost 42 cents, what will 75 pounds cost?

100. What is the cost of 27 weeks' board, if 9 weeks' board cost $27?

101. What will 75 tons of coal cost at $80 for 10 tons?

102. If 56 cents are paid for 7 dozen of eggs, how much must be paid for 27 dozen?

103. If 12 barrels of apples cost 72 dollars, what will 7 barrels cost?

104. How much corn, at 90 cents a bushel, must be given for 27 bushels of rye at 30 cents a bushel?

105. A cistern that holds 120 gallons has a pipe by which 18 gallons can run into it in an hour, and another pipe by which 12 gallons can run out of it in the same time. When both pipes are running how long will it take the cistern to fill?

CLASSIFICATION OF FORMULAS.

NOTE FOR THE TEACHER.-It is very important that the pupils learn the six arithmetical formulas, five of which are used in the fundamental rules; for it is by the means of these six formulas that all problems are solved.

14. FORM. I.-If I have 12 lemons in my pocket and 6 in my hand, in both I have the sum of 12 lemons and 6 lemons, which is 18 lemons.

15. II.-If I have 12 lemons in my pocket and give away 6, I have left the DIFFERENCE between 12 lemons and 6 lemons, which is 6.

16. III.—If 1 lemon costs 6 cents, 12 lemons cost 12 times 6 cents, which are 72 cents.

17. IV. If 6 boys have 12 lemons, 1 boy has one SIXTH of 12 lemons, which is 2 lemons.

18. V.-Since 6 cents will purchase 1 lemon, 12 cents will purchase as many lemons as 6 cents are contained times in 12 cents, which are 2 times.

19. VI.-If a boy has 12 lemons, and he give away 4, he will give away 4 TWELFTHS of his lemons. For formulas III. IV. and V. the following may be used if they are preferred:

(a). III. Twelve lemons will cost 12 times as much as 1 lemon: 1 lemon costs 6 cents, therefore 12 lemons will cost 12 times 6 cents, which are 72 cents.

(b). IV. One boy must have one SIXTH as many apples as 6 boys; 6 boys have 12 apples; therefore one boy must have one SIXTH of 12 apples, which is 2 apples.

(c). V. Since 6 cents will buy 1 lemon, as many lemons can be bought for 12 cents, as the number of times. that 6 cents can be taken from 12 cents, which is 2

N. B. It is not meant that the preceding are the best or the only formulas that can be used. The teacher ought to use his own judgment, and exercise his ingenuity in adapting them to the minds of his pupils. All the principles of the solution of problems are expressed in the six arithmetical formulas, no matter how those principles may be varied or combined. (See Teacher's Manual.)

REDUCTION.

LESSON XXVIII.

20. U. S. Money or currency is the currency used in the United States.

NOTE-1. Dollars are separated from cents and mills by a period,

(); thus $4.732, is read 4 dollars, 73 cents and 2 mills.

2. For description of coins and for other information, see termediate."

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In

PROBLEMS.

1. How many dimes in $4?

FORM.-Since in 1 dollar there are 10 dimes, in $4 there are

4 times 10 dimes, which are 40 dimes; therefore in $4 there are 40 dimes.