EXAMPLES COMBINING THE PRECEDING RULES.

1. How many barrels of flour at $8 a barrel, will pay for 25 tons of coal at $4 a ton, and 36 cords of wood at $3 a cord?

Ans. 26.

2. A grocer bought 12 barrels of sugar at $16 per barrel, and 17 barrels at $13 per barrel; how much would he gain by selling the whole at $18 per barrel?

3. A farmer sold, 300 bushels of wheat at $2 a bushel, corn and oats to the amount of $750; with the proceeds he bought 120

head of sheep at $3 a head, one pair of oxen for $90, and 25 acres of land for the remainder How much did the land cost him per

acre?

Ans. $36.

4. Divide 450+(24—12) × 5 by (906) + (3 × 11) — 18.

Ans. 17. 5. Divide 648 × (32 × 23) ÷ 9 (291015) by 2863 ÷ (4375 ÷ 175) × 42 + 32. Ans. 7129.

6. The product of three numbers is 107100; one of the numbers is 42, and another 34. What is the third number?

Ans. 75.

7. What number is that which being divided by 45, the quotient increased by 72 + 1, the sum diminished by the difference between 28 and 16, the remainder multiplied by 6, and the product divided by 24, the quotient will be 12?

Ans. 450.

8. A mechanic earns $60 a month, but his necessary expenses are $42 a month. How long will it take him to pay for a farm of 50 acres worth $36 an acre?

9. What number besides 472 will divide 251104 without a remainder?

Ans. 532.

10. Of what number is 3042 both divisor and quotient?

Ans. 9253764.

11. What must the number be which, divided by 453, will give Ans. 139180.

the quotient 307, and the remainder 109?

12. A farmer bought a lot of sheep and hogs, of each an equal number, for $1276. He gave $4 a head for the sheep, and $7 a

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 but 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.