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Percentage

To find a certain per cent more or less than a given number.

1. What is 12% more than 250?

250 1.12

500

250

250

12% more than 250 is 112% of 250, which is 280.

280.00

2. What is 15% less than $756?

$756
.85

3780

6048 $642.60

15% less than $756 is 85% of $756, which is $ 642.60.

3. Find 25% more than 72. 4. Find 12% more than 250.

5. Find 60% less than 125. 6. Find 40% less than 475. 7. Find 15% more than 3540. 8. Find 41% more than $215.60. 9. Find 51% less than $164.20. 10. Find 80% less than $2000. 11. Find 100% more than $ 200. 12. Find 35% less than 500 tons. 13. Find 221% more than 800 barrels.

14. Find 163% less than 450 children.

15. Goods which cost $275 are advanced 15%. What is the advanced price?

16. A bill of goods amounting to $324.50 is discounted 20%. What is the amount of the bill as discounted?

Percentage

To find a number which will equal the given number when increased or diminished by the given per cent.

1. What number when increased by 20% of itself equals 240?

240 must be 100% +20%, or 120 % of the required number.

1% of the number is 1 of 240, which is 2, and 100% = 100 times 2, or 200. Or, 240 ÷ 1.20

= 200.

2. What number decreased by 30% of itself equals 35? 35 must be of the number.of the number = 5 and 18 = 50. Or, 35.70 = 50.

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Review Problems

1. What is the length of a square which contains 169 sq. ft.?

2. The length of an oblong is three times its width. It contains 432 sq. ft. How wide is it?

Make a diagram for the oblong.

3. The length of a rectangle is 50% greater than its width. It contains 96 sq. ft. How long is it?

4. What is the length of the edge of a cube whose entire surface is 150 sq. in. ?

What is the surface of one face of the cube?

5. What is the length of the edge of a cube which contains 216 cu. in. ?

6. The length of a square prism is twice its width. It contains 250 cu. in. How wide is it?

Think of the prism as divided into two cubes.

7. The length of a square prism is 3 times its width. It contains 192 cu. in. How long is it?

8. How many yards of carpet, one yard wide, will it take to exactly cover a floor 16 ft. 4 in. long and 15 ft. wide?

9. How many yards of carpet, & of a yard wide, will it take to carpet a floor 22 ft. 6 in. long and 16 ft. wide, if the strips run lengthwise, and no allowance is made for waste in matching?

10. When the fulcrum is between the power and the weight, if the distance from the power to the fulcrum is 61 ft. and the distance from the weight to the fulcrum is 2 ft., how many pounds of power will be necessary to balance a weight of 520 pounds?

11. The weight distance is 28 in. The weight is 1600 lb. The power is 250 lb. Find the power distance.

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Notice that the diagonals of a square divide it into right triangles. See Book II, p. 151.

1. When a square is inscribed in a circle whose radius is 5 inches, what is the length of the diagonal of the square?

2. Find the approximate length of one side of the square.

3. Find the circumference of the circle.

4. What is the area of the square?

Observe that the square is composed of four parts which may be so combined as to make two smaller squares.

5. Find the area of that part of the circle which is outside the square.

Find the area of the whole circle.

6. Find the diameter of a circle whose circumference is 62.832 inches.

7. Find the area of a square inscribed in this circle.

8. Find the difference between the surface of the circle and the surface of the inscribed square.

9. What is the area of the largest square that can be inscribed in a circle whose diameter is 28 inches?

10. What is the area of the largest square that can be inscribed in a circle whose circumference is 314.16?

Review Problems

See p. 207.

1. If the heart beats, on an average, at the rate of 72 strokes a minute, how many times does it beat in a day?

2. At each beat the heart of an average person pumps about 6 ounces of blood. If it beats 72 times a minute, how many tons of blood are moved every day?

3. How many tons of blood are moved in this way every year?

4. The total amount of work done by the heart in a full-sized man, per hour, is about equivalent to lifting a ton to the height of 8 feet. How many tons would be lifted one foot by a force equivalent to the work done by the heart in a year of 365 days?

5. A cannon ball weighing 10 lb. is moving at the rate of 700 ft. per second. Another cannon ball weighing 16 lb. is moving at the rate of 500 ft. per second. What is the ratio of the momentum of the first to that of the second?

See pp. 119, 198, 203.

6. Find the square root of 900.

7. Find the square root of .0625.

8. What is the length of the diagonal of a rectangle 24 ft long, 18 ft. wide?

9. Find approximately the diagonal of a square which is 7 ft. square.

10. The rafters of a house are 30 ft. long and the width of the house is 48 ft. What is the height of the gable?

11. A rectangular farm is 80 rods wide and contains 200 acres. What is its length?

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