8. A manufacturer, owing to a depression in business, offers goods at 121 % discount, but finally sells at a further discount of 8%. Find the entire per cent of discount.

9. What per cent is gained by buying stocks at 15% discount and selling at 5% premium, brokerage %?

10. The tax rate in a certain city is 17 mills on the dollar on a valuation of $66390. Find the tax on a property valued at $12500.

11. A salesman who received a salary of $2400 and $1500 expenses, sold $75000 worth of goods. In addition he received 2% on all sales over $60000. What per cent of the selling price of the goods did it cost the firm to sell them?

12. A man buys through his broker 10 shares of railroad stock (par value $100) at $125 per share. After receiving 5 semiannual dividends of 3% each, he sells the stock at $131. Find the rate per cent of gain on the investment.

13. By selling a piano at 40% above cost, a profit of $150 is realized. For how much must the piano be sold to realize a profit of 56% ?

14. A collector is given a bill of $1500 to collect at 5%. He succeeds in collecting 90 cents on the dollar. Find how much is due his client and how much is the collector's commission.

15. A house and lot cost $6000. The insurance averages $14, taxes $50, and repairs $56 annually. For how much must the house rent per year to realize 6% net on the investment?

16. A house rents for $40 per month, and it costs the owner on an average $125 per year for insurance, taxes, and repairs. If the property yields him 5% net on the investment, find the cost of the house.

RATIO AND PROPORTION

RATIO

1. The quotient of 30 ÷ 10 is 3. Compare 30 with 3 in such a way as to show how many times 3 is contained in 30. What, then, is the relation of 30 to 3?

Ratio is the relation of two similar numbers as expressed by the quotient of the first divided by the second.

2. What is the ratio of 10 to 8? of 12 to 4? of 3 to 6? of 2 yd. to 8 yd.? of $12 to $3.

Since the division of two similar numbers gives an abstract quotient, all ratios are abstract.

The sign of ratio is a colon: placed between the numbers. Thus, the ratio of 12 to 3 is written 12: 3. It is read, "the ratio of 12 to 3." It may be written also 12 ÷ 3, or 12.

The terms of a ratio are the numbers compared. is the antecedent; the second the consequent.

The first

Since the antecedent of a ratio may be regarded as the numerator, and the consequent as the denominator of a fraction, both terms of a ratio may be multiplied or divided by the same number without changing the value of the ratio.

Proportion is an equality of ratios; thus, 12: 68: 4 or 12 is a proportion.

=

equality sign or Thus, 12 6 as

Proportion is generally indicated by the by a double colon between the ratios. 84, is written, 12: 68: 4, or 12: 6:: 8:4.

:

A proportion may be read in two ways; thus, 12:68:4 is read, "The ratio of 12 to 6 is equal to the ratio of 8 to 4," "12 is to 6 as 8 is to 4."

or,

The extremes are the first and the fourth terms of a proportion; the means are the second and the third terms.

In 15:5 12:4, the extremes are 15 and 4; the means, 5 and 12.

=

Find the product of the means; then the product of the extremes :

Observe how the product of the extremes in each proportion compares with the product of the means.

In every proportion the product of the means is equal to the product of the extremes.

Written Work

2. 15:25= x:40

Find the value of x, the unknown term:

1. 36: 6= 24 : x

Then, 36 times x, or 36 x = 144, and once x, or x = 4.

13. If 8 sheep cost $48, how much will 20 sheep cost?

8 sheep cost $48

20 sheep cost $x

Since ratio is the relation of two similar numbers, 8 sheep and 20 sheep form one ratio, and $48 and $x, the other ratio.

Write as the second ratio $48: $x. Since 20 sheep cost more than 8 sheep, $x represents a larger sum than $48. Therefore, as the larger number is the consequent of the second ratio, the larger number must be made the consequent of the first ratio. The proportion, therefore, is, 8 sheep: 20 sheep = $48 : $x

8 x = $960

x = $120

14. It is estimated that 25 men can build a bridge in 18 days. How long at the same rate will it take 15 men to build it?

15. How much will 30 bushels of potatoes cost, if 70 bushels cost $42?

16. It is estimated that 90 men are necessary to grade a certain street in 45 days. If only 81 men are hired to do the work, how long will it take them?

17. The ratio is 3. The first term is 1⁄2 of (6 × 4). What is the second term?

18. A bankrupt's debts are $32000, and his assets $10000. Counting nothing for court costs, how much will be paid on a claim of $6150?

19. If $2.25 is paid to clean 35 square yards of paper, how much at the same rate will it cost to clean 652 square yards?

20. A bakery sells 5¢ loaves weighing 6 oz. when flour is $4. What size loaves should they sell at 5 when flour is $6 per barrel?

5

21. A map is drawn on a scale of 100 miles to of an inch. What distance is represented on the map by of an inch? 22. If the interest on $500 for 6 months is $15, how much is the interest on the same sum for 1 year 4 months? 23. If 6.5 tons of coal cost $55.90, how much will 9.25 tons cost at the same rate?

24. A estimates that he can do a piece of work in 20 days, working 8 hours per day. How long will it take him to do of it, working 10 hours per day?

25. Sound travels 1120 feet per second.

How long will

it take the sound of a cannon to travel 8 miles ?

26. In a stamp canceling machine 1000 letters were canceled in one minute and 20 seconds. If the machine was in operation for 5 minutes and 10 seconds, how many letters at the same rate were canceled?

27. A monument casts a shadow 150 feet long. At the same time a post 3 feet in height casts a shadow 2 feet and 6 inches long. Find the height of the monument.

28. A machine for making pressed brick turns out 7500 brick in 6 days. How large an order for pressed brick can be filled in 25 days?