69. Suppose $1 had been put out, at compound interest, at 7 per cent., the 5th day of October, 1585. How much would it have amounted to on the 1st of December, 1841?

Ans. $3364085.041.

70. A gentleman hires a servant, and promises him, for the first year, only $60 in wages, but for each following year $4 more than for the preceding. How much will the servant receive for the 17th year of his engagement? and how much for all 17 years together? Ans. $124, and $1564.

71. A person had two barrels, and a certain quantity of wine in each. In order to have an equal quantity in each, he poured out as much of the first cask into the second, as it already contained; then, again, he poured out as much of the second into the first as it then contained, and lastly he poured out again, as much from the first into the second, as there was still remaining in it. At last he had 16 gallons of wine in each cask. How many gallons did they contain origin. ally? Ans. The first 22, the second 10 gallons.

72. What is the sum of the cubes of the seven following fractions: 128, 127, 52, 518, 111, 13, and $18? 429, 497 504

525 525 525 525

5

Ans. 6.

The first time he had 39 men

73. A general, wishing to draw up his regiment into a square, tried it in two ways. over; the second, having extended the side of the square by one man, he wanted 50 men to complete the square. What was the number of soldiers in the regiment?

Ans. 1975 men.

74. From a sum of money, $50 more than the half of it is first taken away; from the remainder $30 more than its fifth part; and again, from the 2d remainder $20 more than its fourth part. At last there remained only $10. What was the original sum? Ans, $275.

75. What is the sum of the cubes of the five following frac

357

tions: 359, 343, 38, 378, and 323?

Ans. 6. 76. The siderial revolution of Venus is 224.700817 days. How can this period be represented by smaller numbers?

Ans. By 24, 225, 074, 1573, 2247, 26220, &c.

}

117

77. Find ten numbers, such that the first with of all the rest shall make 845693; the second with of all the rest shall make 845693; the third with of all the rest shall make 845693; the fourth with 1, the fifth with, the sixth with, the seventh with, the eighth with, the ninth with 1, and the tenth with of all the rest, shall make respectively the same number, 845693.

Ans.

485333, 521369, 550853, 575423, 596213.

ERRATA.

"In how many

"A and B can, together, do it in How many days

Question 3d, on page 226, ought to read as follows: ways may the first 25 letters of the alphabet be read in this way?" Question 9th, on page 230, ought to read as follows: together, do a piece of work in 8 days; A and C can, 9 days; and B and C can, together, do it in 10 days. would it require for each to perform the work alone?" There are several other slight errors, which are considered too trifling to need correction in this place.