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126. A merchant sold a quantity of goods for $137.00 less than they cost him, and by doing so lost 23 per cent. How much did the goods cost, and how much did he sell them for?

127. A has tea which he sells B for 10d. per lb. more than it cost him, and in return B sells A cambrick, which cost him 10s. per yd., for 12s. 6d. per yard. The gain on each was in the same proportion. A's tea cost him per lb. ?

What did

Note. B gains 2s. 6d. on a yard, which is of the first cost, consequently 10d. must be of the first cost of the tea ?

128. C has brandy which he sells to for 20 cents per gal. more than it cost him; and D sells C molasses which cost 23 cents per gal. for 32 cents per gal., by which D gains in the same proportion as C. How much did C's brandy cost him per gal. ?

129. A man being asked his age, answered, that if to his age and of his age be added, the sum would be 121. What was his age?

130. A man having put a sum of money at interest at 6 per cent., at the end of 1 year received 13 dollars for interest. What was the principal ?

Note. Since 6 per cent. is of the whole, 13 dollars must be of the principal.

131. What sum of money put at interest for 1 year will gain 57 dollars, at 6 per cent.?

182. A man put a sum of money at interest for 1 year, at 6 per cent., and at the end of the year he received for principal and interest 237 dollars. What was the principal?

06

Note. Since 6 per cent. is, if this be added to the principal it will make 106, therefore $237 must be 10% of the principal. When the interest is added to the principal

the whole is called the amount.

133. What sum of money put at interest at 6 per cent. will gain $53 in 2 years?

Note. 6 per cent. for 1 year will be 12 per cent. for 2 years, 3 per cent. for 6 months, 1 per cent. for 2 months, &c.

134. What sum of money put at interest at 6 per cent will gain $97 in one year and 6 months?

135. What sum of money put at interest at 6 per cent. will amount to $394 in year and 8 months?

136. What sum of money put at interest at 7 per cent. will amount to £183 in 1 year?

137. What sum of money put at interest at 8 per cent. will amount to $137 in 2 years and 6 months?

138. Suppose I owe a man $287 to be paid in one year without interest, and I wish to pay it now; how much ought I to pay him, when the usual rate is 6 per cent. ?

Note. It is evident that I ought to pay him such a sum, as put at interest for 1 year will amount to $287. The question therefore is like those above. This is sometimes called discount.

139. A man owes $847 to be paid in 6 months without interest, what ought he to pay if he pays the debt now, al lowing money to be worth 6 per cent. a year ?

140. A merchant being in want of money sells a note of $100, payable in 8 months without interest. How much ready money ought he to receive, when the yearly interest. of money is 6 per cent.?

141. According to the above principle, what is the differ ence between the interest of $100 for 1 year, at 6 per cent. and the discount of it for the same time?

142. What is the difference between the interest of $500 for 4 years at 6 per cent., and the discount of the same sum for the same time?

Miscellaneous Examples.

A

B

In measuring surfaces, such as land, &c. a square is used as the measure or unit. A square is a figure with four equal sides, and the four corners or angles equal. The square is used because it is more convenient for a measure than a figure of any other form. The figure A B C D is a square. The sides are each one inch, consequently it is called a square

inch.

A figure cne foot long and one foot wide is called a square foot; a figure one yard long and one yard wide is called a square yard, &c.

D

1. If a figure one inch long and one inch wide contains one square inch, how many square inches does a figure one inch wide and two inches long contain? How many square inches does a figure one inch wide and three inches long contain? Four inches long? Five inches long? Seven inches long?

2. In a figure 8 inches long and 1 inch wide, how many square inches? How many square inches does a figure 8 inches long and 2 inches wide contain? 3 inches wide? 4 inches wide? 5 inches wide? 8 inches wide?

3. If a figure 1 foot wide and 1 foot long contains 1 squaro foot, how many square feet does a figure I foot wide and 2 feet long contain ? How many square feet does a figure 1 foot wide and 3 feet long contain? 5 feet long? 9 feet long? 15 feet long?

4. In a figure 9 feet long and 1 foot wide, how many square feet? How many square feet does a figure 9 feet long and 2 feet wide contain? 3 feet wide? 5 feet wide? 7 feet wide? 9 feet wide?

5. How many square inches does a figure 13 inches long and 1 inch wide contain? 2 inches wide? 3 inches wide? 8 inches wide?

6. How many square feet does a figure 16 feet long and 1 foot wide contain? 2 feet wide? 3. feet wide? 5 feet wide? 8 feet wide? 13 feet wide?

In the above examples supply yards, rods, furlongs, and miles, instead of inches and feet, and perform them again.

7. What rule can you make for finding the number of square inches, feet, yards, &c. in any rectangular figure?

Note. A figure with four sides, which has all its angles alike or right angles, is called a rectangle, and a rectangle is called a square when all the sides are equal.

8. How many square feet in a room 18 feet long and 13 feet wide ?

9. How many square feet in a piece of land 143 feet long and 97 feet wide?

10. How many square rods in a piece of land 28 rods long and 7 rods wide?

11. A piece of land that is 20 rods long and 8 rods wide, or in any other form containing the same surface, is called an acre. How many square rods in an acre

12. How wide must a piece of land be that is 17 rods long to make an acre?

13. How many square inches in a square foot; that is, in a figure that is 12 inches long and 12 wide?

14. How much in length, that is 8 inches wide, will make a square foot?

15. How many square feet in a square yard?

16. How many square yards in a square rod?

17. How many square inches in a square yard?

18. A piece of land 20 rods long and 2 rods wide, or in any other form which contains the same surface, is called a rood. How many square rods in a rood?

19. How many roods make an acre?

20. Find the numbers for the following table.

[blocks in formation]

21. How many square inches in a square rod ? 22. How many square yards in an acre?

23. How many square inches in an acre?

24. How many square feet in 1728 square inches ?

25. In 236 square poles how many acres?

26. In 201,283,876 square inches, how many acres? 27. How many square rods in a square mile?

28. How many acres in a square miles

20. The whole surface of the globe is estimated at about 198,000,000 square miles. How many acres on the surface of the globe?

30. How many square inches in a board 15 inches wide and 11 feet long? How many square feet?

31. How many acres in a piece of land 183 rods long and 97 rods wide?

32. How many square inches in a yard of carpeting that is 2 ft. 3 in. wide? How many yards of such carpeting will it take to cover a floor 19 ft. 4 in. long and 17 ft. 2 in. wide?

To measure solid bodies, such as timber, wood, &c., it is necessary to use a measure that has three dimensions, length, breadth, and depth, height, or thickness. For this a measure is used in which all these dimensions are alike. Take a block, for example, and make it an inch long, an inch wide, and an inch thick, and all its corners or angles alike; this is called a solid or cubic inch; so a block made in the same way having each of its dimensions one foot, is called a solid or cubic foot.

33. If a block 1 inch wide and 1 inch thick and 1 inch long contains 1 solid inch, how many solid inches does such a block that is 2 inches long contain? 3 inches long? 4 inches long? 5 inches long? 8 inches long?

34. How many solid inches does a block that is 1 foot long, I inch thick, and I inch wide contain? How many inches does such a block that is 2 inches wide contain? 3 inches wide? 4 inches wide? 5 inches wide? 8 inches wide ?

35. How many solid inches does a block 2 inches long, 2 inches wide, and 1 inch thick contain? 2 inches thick ?

36. How many solid inches does a block 4 inches long, 3 inches wide, and 1 inch thick contain? 2 inches thick? 3 inches thick ?

37. How many cubic inches in a block 10 inches long, 8 inches wide, and 1 inch thick? 2 inches thick ? 3 inches thick 5 inches thick? 7 inches thick ?

38. How many cubic inches in a block 18 inches long, 13 inches wide, and 1 inch thick? 5 inches thick? 11 inches thick ?

In the above examples supply feet instead of inches, and do them over again.

39. What rule can you make for finding the number of solid inches or feet in any regular solid body?

40. How many solid inches in a block 12 inches long, 12 inches wide, and 12 inches thick; that is, in a solid foot?

41. A pile of wood 8 feet long, 4 feet wide, and 4 feet high, or in any other form containing an equal quantity, is called a cord of wood. How many solid feet in a cord? 42. Find the numbers for the following table.

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