235. MISCELLANEOUS PROBLEMS IN APPLICATIONS OF

PERCENTAGE.

1. A dealer who had marked goods 50% above the cost, sold them after deducting 10% from the marked price. His profit on that sale was what per cent of the cost of the goods?

2. By selling a suit of clothes for $7.20 I would lose an amount equal to 10% of the cost. For what must I sell the suit to gain a sum equal to 10% of the cost?

3. I sold goods at a loss of 7%. My actual loss was $3.50. What was the cost of the goods?

4. The real value of a stock of goods was $8250. They were insured for $5500. A fire occurred and the salvage amounted to only $575. If the insurance company promptly settles in accordance with the above facts what is the actual loss to the owner of the goods?

5. If I sell goods on a commission of 12%, what must be the amount of my sales in order that I may receive an annual salary of $2500?

6. A school numbers 140 pupils. The absence for one week was as follows: Monday, 3 days; Tues., 5 days; Wed., 4 days; Thurs., 5 days; Friday, 3 days. (a) What was the per cent of absence? (b) What was the per cent of attendance?

7. Sold a horse for $120 and gained 25%. What did the horse cost me ?

8. When the cost is of the selling price what is the gain per cent?

9. When the selling price is of the cost what is the loss. per cent?

Algebra.

236. MISCELLANEOUS PROBLEMS.

1. In a school there are times as many boys as girls. boys?

896 pupils. There are three How many girls? How many

2. A man had 235 sheep. In the second flock there were

15 more sheep than in the first. were 20 fewer than in the first. flock?

In the third flock there

How many sheep in each

NOTE.-Let x = the number in the first flock; then x + 15 = the number in the second, and x 20, the number in the third.

3. A man owns three farms. In the second there are half as many acres as in the first. In the third there are twice as many acres as in the first. In all there are 560 acres. How many acres in each farm?

4. In an apple and pear orchard containing 296 trees, there were 5 more than twice as many apple trees as pear trees. How many of each kind?

5. To a number I add one half of itself and 15, and have 150. What is the number?

6. From three times a number I subtract

and 5, and have 37 remaining.

of the number

What is the number?

2x

NOTE. Let x = the number; then 3x (+5)=37. On

removing the parenthesis, what signs must be changed? See page 207, II.

7. If to three times a number I add of the number and 18, the sum will be 238. What is the number?

8. Two thirds of a number is equal to the number decreased by 56. What is the number?

Algebra.

237. MISCELLANEOUS PROBLEMS.

1. A is 50 years old. B is 20 years old. years will A be only twice as old as B?

In how many

NOTE. Let x = the number of years; then (20 + x) × 2 = 50+x.

2. Find four consecutive numbers whose sum is 150. NOTE. Let x = the first; then x+1 = the second; x + 2 = the third, etc.

3. Find three consecutive numbers whose sum is 87. 4. Two numbers have the same ratio as 2 and 3 and their sum is 360. What are the numbers ?

5. Two numbers have the same ratio as 3 and 4, and their sum is 168. What are the numbers?

6. Two numbers have the same ratio as 2 and 5, and their difference is 87. What are the numbers?

7. A has $350. B has $220.

B has $220.

How many dollars must

A give to B so that each may have the same sum ?

NOTE.—Let x = the number of dollars that must be given by A

to B; then 220 + x = 350 · x.

8. C has $560. D has $340.

C give to D so that each may have

How many dollars must the same sum?

9. E has $630. F has $240. How many dollars must E give to F so that E will have exactly twice as many dollars as F?

10. The fourth and the fifth of a certain number are together equal to 279. What is the number?

11. The difference between 1 fourth and 1 fifth of a certain number is 28. What is the number?

Geometry.

238. How MANY DEGREES IN EACH ANGLE OF A REGULAR

2. The sum of the angles of one triangle is equal to right angles, then the sum of the angles of 6 triangles is equal to

right angles.

3. But the sum of the central angles in Fig. 2 (a + b + c +d+e+ƒ) is equal to right angles; then the sum of all the other angles of the six triangles is equal to 12 right angles less 4 right angles, or 8 right angles = 720°. But the angular space that measures 720°, as shown in Fig. 2, is made up of 12 equal angles; so each one of the angles is one 12th of 720°, or 60°. Two of these angles, as 1 and 2, make one of the angles of the hexagon; therefore each angle of the hexagon measures 2 times 60°, or 120°.

4. Using the protractor, construct a regular hexagon, making each side 2 inches long.

Observe that since all the angular space about a point is equal to 4 right angles, or 360°, and since the space around the central point of the hexagon is divided into 6 equal angles, each of these angles is an angle of (360° ÷ 6) 60°. But each of the other angles of these triangles has been shown to be an angle of 60°; so each triangle is equiangular. Are the triangles equilateral?

239. Miscellaneous Review.

1. A man buys goods for $60 and sells them for $75. He gains dollars.

(a) The gain equals what part of the cost? What %? (b) The gain equals what part of the selling price? What per cent?

(c) The cost equals what part of the selling price? What per cent?

2. When the cost is 2 thirds of the selling price what is the per cent of gain?

3. When the selling price is 2 thirds of the cost what is the per cent of loss?

4. Bought for $200 and sold for $300. What was the per cent of gain?

5. Bought for $300 and sold for $200. What was the per cent of loss?

6. A tax of 15 mills on a dollar was levied in a certain town, the assessed value of the taxable property being $475,250. If 5% of the tax is non-collectable and if the collector is allowed 2% of the amount collected, for his services, how much will be realized from the levy?

7. Which is the greater discount, "20 and 10 and 5 off” or "35 off"?

8. A sold goods for B on a commission of 15%. His sales for a certain period amounted to $780. If the goods cost B exactly $600 was B's net profit more or less than 10%?

9. A offers rubber boots at "50 and 20 off"; B offers them at "20 and 50 off." The quality and list price being the same, which offer shall I accept?