WRITTEN PROBLEMS 1. Mr. Nason and Mr. Parker formed a partnership, Mr. Nason furnishing $3000, and Mr. Parker $5000. They gained $2400. Find each partner's profit. and B $6000. } of $2400, or $900 of $2400, or $1500 2. A and B engaged in business, A investing $4500, At the end of the year they divided a profit of $2940. What was the share of each? 3. Mr. Spencer and Mr. Waldron shipped potatoes to the market together, Mr. Spencer shipping 240 bushels, and Mr. Waldron 420 bushels. The potatoes were sold for $429. After deducting expenses of shipping and selling, amounting to 8 cents a bushel, what amount should each receive? 4. Two men in business one year earned $6440 on a capital of $10,400, of which one furnished $5600, and the other the balance. Apportion the gain. 5. Three men formed a syndicate to purchase a tract of land for $120,000. A put in $34,000, B. $40,000, C $46,000. At the end of the year they were obliged to sell the land for $100,000. What was the loss to each individual? 6. What is the share of each of three partners in a gain of $3750, if the first and second invest equal capital, and the third as much as the first and second together? 7. The total gain was $840. A's capital was $1200, B's as much as A's, and C's as much as B's. What was each one's gain? 8. What amount of a capital of $3900 was contributed by two partners whose profits were, respectively, $480 and $560? 9. What amount of the capital of $4200 has each partner invested, if out of a gain of $840 one receives $520? 10. Five men hired a pasture for their cows for $100, and paid $15.50 for repairing the fences. What was each one's share of the total expense, if they pastured cows as follows: A, 5 cows for 10 weeks; B, 3 cows for 12 weeks ; C, 4 cows for 9 weeks; D, 1 cow for 12 weeks; and E, 2 cows for 10 weeks? 11. A vessel costing $9000, and insured for its value, was lost at sea. Apportion the insurance money among the owners, who owned 4, 3, and 2 shares, respectively. 12. Mr. Barnard, Mr. Sears, and Mr. White built a fishing vessel at a cost of $13,000, contributing $6000, $4500, and $2500, respectively, and agreeing to divide the profits after the vessel had made 25 trips. The vessel averaged 36,000 pounds of fish to a trip, for which was received an average price of $2.75 per hundredweight. The expenses were $6750; of the net receipts went to the crew, and Find each owner's gain. This was what If there were 16 men in the to the owners. per cent of the investment? crew, how much did each receive? RATIO Ratio is the relation of one number to another of the same kind. Ratio is expressed by the sign written between the two numbers, and is equivalent to the sign +. Thus, the ratio of 8 to 4 is written 8: 4, and means 8 ÷ 4, or 2. The numbers compared are the terms of the ratio. The first term is the antecedent, and the second the consequent. Thus, in the ratio 4: 8, 4 is the antecedent, and 8 the consequent. The two terms taken together form a couplet. At sight, tell the ratios: Proportion is an equality of ratios. Thus, 8:46:3, or & = §. This means that the ratio of 8 to 4 (2) is equal to the ratio of 6 to 3 (2); or, that the quotient of 84 is equal to the quotient of 6 ÷ 3. = The sign is sometimes used instead of the sign between the two ratios. Thus, 8:4::6:3; and the proportion is read, 8 is to 4 as 6 is to 3. At sight, test by comparing the ratios : The first and the last terms of a proportion are the extremes, and the two middle terms the means. In every proportion the product of the means equals the product of the extremes. Thus, in the proportion 8:46:3, the product of the means (4 x 6), 24, equals the product of the extremes (8 × 3), 24. 11. At sight, test the proportions in examples 1 to 10 by comparing the product of the extremes with the prod uct of the means. Since the product of the means equals the product of the extremes, a missing extreme is found by dividing the product of the means by the given extreme. 12. Find the missing mean in 8: ?= 6:3. 13. Tell how to find a missing mean. Find the missing terms: Express the equality as in a proportion. Express the equality 34. Write a ratio equal to 12: 4. of these ratios. Arrange the terms 35. Write a fraction equal to . of these fractions, and arrange the terms as in a proportion. 36. What number has the same relation to 12 as 18:6? Express this fact in a proportion. 37. Write two couplets whose ratios are 8. Express their equality. 38. Write a proportion the product of whose means is 48. 39. Write a proportion the product of whose extremes is 36. WRITTEN PROBLEMS 1. If 12 tons of hay cost $222, what will 14 tons cost? SOLUTION 12:14:: 222: ? Since the answer is to be in dollars, we make 222 the third term. It is evident that the same relation must exist between the cost of 12 tons and the cost of 14 tons as exists between 12 tons and 14 tons. Since 14 tons cost more than 12 tons, the first ratio must read 12:14, because, if the fourth term is to be greater than the third term, the second term must be greater Ans. $259. than the first. 7 37 14 × 222 12 β = 259 |