head for the hogs; what was the whole number purchased, and how much was the difference in the total cost of each?

Ans. 232 purchased; $348 difference in cost.

13. According to the census of 1850 the total value of the tobacco raised in the United States was $13,982,686. How many school-houses at a cost of $950, and churches at a cost of $7500, of each an equal number, could be built with the proceeds of the tobacco crop of 1850? Ans. 1654, and a remainder of $6386.

14. The entire cotton crop in the United States in 1859 was 4,300,000 bales, valued at $54 per bale. If the entire proceeds were exchanged for English iron, at $60 per ton, how many tons would be received?

15. The population of the United States in 1850 was 23,191,876. It was estimated that 1 person in every 400 died of intemperance. How many deaths may be attributed to this cause in the United States, during that year?

16. In 1850, there were in the State of New York, 10,593 public schools, which were attended during the winter by 508464 pupils; what was the average number to each school?

Ans. 48.

17. A drover bought a certain number of cattle for $9800, and sold a certain number of them for $7680, at $64 a head, and gained on those he sold $960. How much did he gain a head, and how many did he buy at first?

Ans. Gained $8 per head; bought 175. 18. A house and lot valued at $1200, and 6 horses at $95 each, were exchanged for 30 acres of land. At how much was the land valued per acre?

19. If 16 men can perform a job of work in 36 days, in how many days can they perform the same job with the assistance of 8 more men?

Ans. 24.

20. Bought 275 barrels of flour for $1650, and sold 186 barrels of it at $9 a barrel, and the remainder for what it cost. How much was gained by the bargain?

Ans. $558.

21. A grocer wishes to put 840 pounds of tea into three kinds of boxes, containing respectively 5, 10, and 15 pounds, using the

same number of boxes of each kind. How many boxes can he fill? Ans. 84. 22. A coal dealer paid $965 for some coal. He sold 160 tons for $5 a ton, when the remainder stood him in but $3 a ton. How many tons did he buy? Ans. 215.

23. A dealer in horses gave $7560 for a certain number, and sold a part of them for $3825, at $85 each, and by so doing, lost $5 a head; for how much a head must he sell the remainder, to gain $945 on the whole? Ans. $120.

24. Bought a Western farm for $22,360, and after expending $1742 in improvements upon it, I sold one half of it for $15480, at $18 per acre. How many acres of land did 1 purchase, and at what price per acre?

PROBLEMS IN SIMPLE INTEGRAL NUMBERS.

124. The four operations that have now been considered, viz., Addition, Subtraction, Multiplication, and Division, are all the operations that can be performed upon numbers, and hence they are called the Fundamental Rules.

125. In all cases, the numbers operated upon and the results obtained, sustain to each other the relation of a whole to its parts. Thus,

I. In Addition, the numbers added are the parts, and the sum or amount is the whole.

II. In Subtraction, the subtrahend and remainder are the parts, and the minuend is the whole.

III. In Multiplication, the multiplicand denotes the value of one part, the multiplier the number of parts, and the product the total value of the whole number of parts.

IV. In Division, the dividend denotes the total value of the whole number of parts, the divisor the value of one part, and the quotient the number of parts; or the divisor the number of parts, and the quotient the value of one part.

126. Every example that can possibly occur in Arithmetic, and every business computation requiring an arithmetical opera

tion, can be classed under one or more of the four Fundamental

Rules, as follows:

I. Cases requiring Addition.

There may be given

1. The parts.

2 The less of two numbers and

their difference, or the sub

trahend and remainder,

To find

the whole, or the sum total.

the greater number or the minuend.

127. Let the pupil be required to illustrate the following problems by original examples.

Problem 1. Given, several numbers, to find their sum.

Prob. 2. Given, the sum of several numbers and all of them ut one, to find that one.

Prob. 3. Given, the parts, to find the whole.

Prob. 4. Given, the whole and all the parts but one, to find that one.

Prob. 5. Given, two numbers, to find their difference.

Prob. 6. Given, the greater of two numbers and their difference, to find the less number.

Prob. 7. Given, the less of two numbers and their difference, to find the greater number.

Prob. 8. Given, the minuend and subtrahend, to find the remainder.

Prob. 9. Given, the minuend and remainder, to find the subtrahend.

Prob. 10. Given, the subtrahend and remainder, to find the minuend.

Prob. 11. Given, two or more numbers, to find their product. Prob. 12. Given, the product and one of two factors, to find the other factor.

Prob. 13. Given, the continued product of several factors and all the factors but one, to find that factor.

Prob. 14. Given, the factors, to find their product.

Prob. 15 Given, the multiplicand and multiplier, to find the product.

Prob. 16. Given, the product and multiplicand, to find the multiplier.

Prob. 17. Given, the product and multiplier, to find the multiplicand.

Prob. 18. Given, two numbers, to find their quotients.

Prob 19. Given, the divisor and dividend, to find the quotient. Prob. 20. Given, the divisor and quotient, to find the dividend. Prob. 21. Given, the dividend and quotient, to find the divisor. Prob. 22. Given, the divisor, quotient, and remainder, to find the dividend.

Prob. 23. Given, the dividend, quotient, and remainder, to find the divisor.

Prob. 24. Given, the final quotient of a continued division and the several divisors, to find the dividend.

Prob 25. Given, the final quotient of a continued division, the first dividend, and all the divisors but one, to find that divisor.

Prob. 26. Given, the dividend and several divisors of a continued division, to find the quotient.

Prob. 27. Given, two or more sets of numbers, to find the difference of their sums.

Prob. 28. Given, two or more sets of factors, to find the sum of their products.

Prob. 29. Given, one or more sets of factors and one or more numbers, to find the sum of the products and the given numbers. Prob. 30. Given, two or more sets of factors, to find the difference of their products.

Prob. 31. Given, one or more sets of factors and one or more numbers, to find the sum of the products and the given number or numbers.

Prob 32. Given, two or more sets of factors and two or more other sets of factors, to find the difference of the sums of the products of the former and latter.

Prob 33. Given, the sum and the difference of two numbers, to find the numbers.

ANALYSIS. If the difference of two unequal numbers be added to the less number, the sum will be equal to the greater; and if this sum be added to the greater number, the result will be twice the greater number. But this result is the sum of the two numbers plus

their difference

Again, if the difference of two numbers be subtracted from the greater number, the remainder will be equal to the less number; and if this remainder be added to the less number, the result will be twice the less number. But this result is the sum of the two numbers minus their difference.

Hence,

I. The sum of two numbers plus their difference is equal to twice the greater number

II. The sum of two numbers minus their difference is equal to twice the less number.