NOTE. The mark for dollars is usually thus, $, which always denotes that the number OVER, or to the LEFT of which it is placed, is so many dollars, as will be more fully

$

explained in COMMERCIAL ARITHMETIC; as, 6, or $6, is 6 dollars. Other commodities, for the present, will be distinguished by placing over, or on the right of the number, their first letter, or letters; as, 6 cts. for 6 cents; 6 bus. for 6 bushels, &c.

19. If a piece of land 183 feet wide, 175 feet deep, be sold at auction for $25875, what is the worth of a lot 413 feet wide, 224 feet deep, of land equally valuable?

Given quantity, 1835 ft., 175-1405 ft., i. e., 75 X 8

1405

Equivalent, 25875-51751 Dols.

2

Required quantity, 413=124 ft., 224=1124 ft., i. e.,

124 1124

20. How many blocks of an inch in length, breadth, and thickness, would it take to fill a box 12 inches square?

Given quantity, in. long, in. wide, 1 in. deep, i. e.,

Equivalent, 1 block.

Required quantity, 12 in. long, 12 in. wide, 12 in. thick,

i. e., 12 x 12 × 12.

le'th. wid. thick.

We

The preceding examples are sufficient to prove, that RATIONAL EQUATIONS present an intelligent mode of conducting Arithmetical calculations, and that THEY may be applied in all cases where it is possible to form a PROPORTION. will now introduce some questions, to be performed by the pupil, in the solution of which the pupil may adopt the following

RULE for finding RATIONAL EQUIVALENTS.

I. First, find the GIVEN QUANTITY; second, its EQUIVALENT; and, third, the REQUIRED QUANTITY, and reduce the mixed numbers to improper fractions, and the whole numbers to the fractional form; then,

II. Place the GIVEN QUANTITY on the left of (=) the sign of equality, [separating the terms by dots (),] and its EQUIVALENT on the right, and call this expression the first, or GIVEN EQUATION, under which draw a line; and,

III. At a convenient distance below THIS, place the second equation, (formed from the first by placing UNITS on the left, and transferring the terms, greater than a unit to the right, inverting the DIRECT TERMS, i. e., changing their signs,) and call it the SIMPLE EQUATION, under which draw a line as before; and,

IV. Place the required quantity in BоTH members of the simple equation, (taking care to INVERT the inverse terms,

before placing them in the right hand member,) and we shall then have the REQUIRED EQUATION, the right hand member of which, reduced to its simplest form, will give the RATIONAL EQUIVALENT of the required quantity, or the ANSWER sought.

NOTE.-When the GIVEN QUANTITY consists of a UNIT, or of UNITS, the IIIrd. clause of the RULE will be unneces sary, and only two equations will be required for a solution. According to the above RULE, and similar to the Examples from page 103 to page 112, inclusively, it is required to solve the following

QUESTIONS PRODUCING RATIONAL EQUATIONS.

1. Bought 12 pounds of butter at 18 cents a pound, what did it come to? What would be the cost of 15 pounds at

that rate?

2. At 25 cents a yard, what would 20 yards of chintz cost? What would 25 yards cost?

3. Suppose a horse could travel 45 miles in a day, how far would he travel in 17 days at that rate?

4. What would 25 pounds of tea come to, at 75 cents a pound?

5. Bought 25 quires of paper, at 24 cents a quire, what did they come to? What would 45 quires come to, at that

rate?

6. If 1 cow cost 25 dollars, what will 37 cows cost at that rate? What would 63 cost? What would 84 cost?

7. If a railroad car will travel 24 miles in an hour, how far will it travel in 53 hours?

8. If a steamship will travel 216 miles in a day, how far will she travel in 25 days?

9. If a piece of muslin contain 31 yards how many yards would 16 pieces contain?

10. If 1 yard of muslin is worth 125 cents, what will 96 yards of the same muslin cost?

11. If 1 yard of broad cloth cost 83 dollars what will 12 yards cost? What will 36 yards cost?

12. If 1 yard of calico cost 183 cents, what will 12§ yards cost? What will 25 yards cost?

13. At 8 cents per pound, what will 9 pounds of sugar cost? What will 12 pounds cost?

14. If 5 yards of cloth cost 15 dollars, what will 1 yard cost? What will 2 yards cost?

15. If 4 pounds of rice cost 12 cents, what will 2 pounds cost? What will 3 pounds cost?

16. If 6 pairs of boots cost 24 dollars, what will 4 pairs cost? What will 7 pairs cost?

17. If 5 reams of paper cost 25 dollars, what will 8 reams cost? What will 11 reams cost at that rate?

18. Bought 9 yards of muslin for 108 cents, what would 7 yards cost at that rate?

19. Bought 12 pounds of ham for 96 cents, what would be the cost of 16 pounds, at that rate?

20. If I may ride 42 miles for 210 cents, how far may I ride for 336 cents?

21. If 25 pounds of rice cost 100 cents, what would 9 pounds cost at that rate? What would 18 pounds cost? What would 27 pounds cost?

22. If 14 pounds of sugar cost 84 cents, what would 17 pounds cost at that rate?

23. A man charged 96 cents for a horse, to ride 16 miles, how far might he ride for 672 cents?

24. If 37 pounds of sugar cost 296 cents, what would 56 pounds cost at the same rate?

25. If 49 tons of iron cost 4900 dollars, how much is that a ton? What will 450 tons cost at the same rate?

26. If 75 yards of cloth cost 600 dollars, what will 350 yards cost? What will 749 yards cost?

27. A gentleman bought a piece of broad cloth at auction, which measured 31 yards, for 167 dollars; and, being pleased with his bargain, he purchased 97 yards at the same

rate, what did the last purchase come to? What would be the cost of 127 yards at this rate?

28. If of a yard of cloth cost 3 dollars, what would 1 yard cost? What would 5 yards cost? What would 7

yards cost?

29. If of a pound of sugar cost 6 cents, what would 1 pound cost? What would 7 pounds cost?

30. If of a yard of muslin cost 9 cents, what would 1 yard cost? What would 25 yards cost?

45

31. If of a pound of tea cost 52 cents, what would 1 pound cost? What would 7 pounds cost? What would 15 pounds cost? What would 28 pounds cost?

32, If of a pound of young hyson cost 75 cents, what would 1 pound cost? What would 35 pounds cost?

33. If of a pound of chocolate cost 18 cents, what is that a pound? What would be the cost of 21 pounds, at that rate?

34. If of a yard of chintz cost 28 cents, what would 7 yards cost? What would 15 yards cost?

35. Bought of a yard of calico for 24 cents, and afterward took a piece containing 37 yards, at the same rate, what did it cost?

36. If of a pound of butter cost

of a dollar, what would 1 pound cost? What would 12 pounds cost? of a pound of indigo cost 1 dollar and of a of a dollar, what would 7 pounds cost, at the

37. If dollar, i. e., same rate?

38. What is the cost of of a pound of black tea, at the rate of 1 pound and of a pound, i. e., of a pound for 52 cents? At the same rate, what would be the cost of of a pound?

39. If of a pound of green tea cost 13 of a dollar, what would of a pound cost?

16

40. If of a yard cost 11 of a dollar, what would of a yard cost? What would 1 of a yard cost?