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Review Problems

1. A commission merchant sold 200 barrels of flour at $4.50 a barrel on a commission of 3%. What was the amount of his commission?

2. An agent received $20 for selling potatoes at 50 cents a bushel on a commission of 4%. How many bushels did he sell?

3. If I buy a gross of pencils for $2.50, and sell of them at the rate of 2 for 5 cents, and the remainder for 3 cents each, what will be the profit?

What is the interest of:

4. $1 for 4 yr. at 6%?

6. $5 for 31 yr. at 6%?

5. $3 for 2 yr. at 6%?

7. $12 for 2 yr. at 4%?

8. The distance from the earth to the moon is 240,000 miles, and to the sun 93,000,000 miles. How farther is it to the sun than to the moon?

How many times

9. Find about how far the earth travels in its revolution around the sun.

Find the length of its path, which is nearly the circumference of a circle.

10. How many times the distance which the moon traverses in its revolution around the earth is the distance which the earth traverses in its revolution around the sun?

11. How many grains are there in 2 lb. 6 oz. 8 pwt.? 12. How many Avoirdupois pounds will it take to make 175 Troy pounds?

13. If a Fahrenheit thermometer should fall 15° in a night, how much would a Centigrade thermometer fall?

14. When the Fahrenheit thermometer registers 8° below zero, what does the Centigrade thermometer register?

Measurements

Review p. 45, and Book II, pp. 214, 227, 244. Find the measurements of the regular prism:

Surface of ends = ? Find the lateral surface. Entire surface?

1. The ends are 8 in. square.
2. 9 in. square; 16 in. long.
3. 2 ft. 4 in. square; 4 ft. long.
4. 3 ft. 2 in. square; 6 ft. long.

Entire surface = ?

Find the measurements of the cylinder 3 ft. long:

5. The diameter is 15 in. Find the circumference. 6. The radius is 10 in. Find the lateral surface. 7. The circumference is 42 in. Find the diameter. 8. The circumference is 38 in. Find the radius.

Find the lateral surface of the regular pyramid: 9. The base is 4 ft. square.

10. The base is 63 ft. square.

61

The slant height is 6 ft.

The slant height is 10 ft.
Slant height

11. Base a triangle. Each side 18 in. 3 ft.

12. Base a triangle. Each side 3 ft. Slant height 5 ft. 2 in.

Find the measurements of the cone. The slant height is

40 inches:

13. Diameter of base is 20 in. Find its circumference. 14. Circumference of base is 18 in. Find its radius. 15. Radius of base is 8 in. Find the lateral surface. 16. Diameter of base is 2 ft. Find the lateral surface.

Find the measurements of the sphere:

Find the circumference.

17. The diameter is 25 in.

18. The circumference is 6 ft. Find the diameter.

19. The diameter is 5 ft. 20. The radius is 18 in.

Find the surface.

Find the surface.

Original Problems

Make problems and solve them:

1. Light travels at the rate of about 186,000 miles a second.

2. Sound travels in the air at the rate of about 1100 feet per second.

3. The sound of thunder is heard 10 seconds after the flash of the lightning is seen.

4. The planet Jupiter is 475,700,000 miles from the sun. 5. A note of $300 gained $ 3.75 at 6%.

6. I receive an annual income of $400 from a certain investment.

7. A manufacturing druggist buys quinine enough to make 10,000 2-grain pills.

8. A can do of a piece of work in an hour, and B of it in an hour.

9. A silver manufacturer buys silver enough to make 100 doz. silver spoons, each spoon weighing 2 oz. 12 pwt.

10. An apothecary buys 10 lb. of drugs by Avoirdupois weight, and sells them in prescriptions by Apothecaries' weight.

11. An auctioneer sells goods to the amount of $ 850 on a commission of 3%.

12. A commission merchant received $60 as his commission for selling goods on a commission of 5%.

13. An agent remitted $114 after deducting his commission of 5%.

14. A Fahrenheit and a Centigrade thermometer hang near each other. The Fahrenheit thermometer indicates 12°.

15. A field in the form of a trapezoid is 60 rods long, 12 rods wide on one of the parallel sides, and 151⁄2 rods on the other.

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Algebra

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In the equation the second member may be changed so that the equation will be . Then 8 = 8. When all the terms of an equation are similar fractions, the numerators of all the terms will form a true equation.

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The denominators may also be removed by multiplying both members of the equation by 4, the largest number containing all the denominators. This has the same effect as changing all the members to similar fractions.

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9. Two thirds of a certain number, increased by 6, would equal 30. Find the number.

10. If to a certain number one half of itself and one fourth of itself are added, the sum will be 35. Find the number.

11. The sum of two numbers is 27. The second number is four fifths of the first. What are the numbers?

Algebra

A parenthesis inclosing two or more quantities indicates that the quantities inclosed are to be regarded as a single quantity. The combined value of the quantities is to be added or subtracted according to the sign before the parenthesis. When the parenthesis is removed, care must be taken that the value of the whole expression is not changed.

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When there is a plus sign before the parenthesis the value of the expression is not changed by removing the parenthesis. To add 6 and subtract 2 produces the same effect as to add the difference between 6 and 2.

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To subtract the difference between 6 and 2 is not the same as to subtract both 6 and 2. If 6 is first subtracted, 2 must then be added to correct the error. If both 6 and 2 are to be subtracted, the minus sign must be placed before both when the parenthesis is removed.

For these reasons, in removing a parenthesis which is preceded by the minus sign, the signs of all the terms within the parenthesis must be changed.

If the first term within the parenthesis has no sign, plus is understood.

Remove the parentheses and find value of x:

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