more of the first kind must be taken. Hence, the proportion is 1+11=21 lbs. worth 7 cents, to 2 lbs. worth 10 cents, to 1 lb. worth 12 cents. Ex. 3. A grocer has four kinds of tea, worth respectively 50, 60, 70, and 90 cents a pound. In what proportion must they be taken to make a mixture worth 80 cents a pound ? Solution. On a pound of the first kind there is a gain of 30 cents; on a pound of the second, a gain of 20 cents; on a pound of the third, a gain of 10 cents; and, hence, on a pound of each of these three kinds a gain of 30+20+10=60 cents. On 1 pound of the fourth kind there is a loss of 10 cents; and, hence, to counterbalance the 60 cents gain, 6 pounds of the fourth kind must be taken. The proportion is, therefore, 1 lb. of the first kind, to 1 lb. of the second, to 1 lb. of the third, to 6 pounds of the fourth or multiples of these numbers. Ex. 4. A farmer has oats worth 40 cents a bushel; corn, worth 50 cents; rye, worth 70 cents; and wheat, worth 90 cents. How must they be mixed that the mixture may be worth 60 cents ? Solution.-On each bushel of oats there is a gain of 20 cents; on each bushel of wheat a loss of 30 cents. Hence, he must take 1 bushel of oats to 1 bushel of wheat. On each bushel of corn there is a gain of 10 cents; on each bushel of rye, a loss of 10 cents. Hence, he must take 1 bushel of corn to 1 of rye. Proportion, 1, 1, 1, 1. - Note. In the above solutions, it will be observed that the ingredients are combined, two and two, in such quantities as to make gains and losses EQUAL. 4th Example. or Ans. Verifications. 3 |30 × 40=1200 3x40-120 10×50 500 1x50= 50 10x70 700 1x70 70 +-Topi Ans., 140. 30 50 10 60 70) 10 ÷10= 1 1 90 20 2 20 × 90=1800 70 X 2×90=180 4200 7 )420 60 60 Write the values or qualities of the ingredients in a column, and the value or quality of the mixture at the left hand. Link each number in the column that is LESS than the value or quality of the mixture with one that is GREATER, or the reverse. Then find the difference between the value or quality of the mixture and that of each ingredient, and place the same opposite the number with which it is connected. The number, or the sum of the numbers, opposite the value or quality of each ingredient, will denote the amount of the same to be taken. Remark. Since equi-multiples of quantities have the same relation to each other as the quantities themselves, it follows that any equi-multiples of these numbers will also satisfy the conditions of the problem. Ex. 5. A merchant has teas worth 60, 75, 80, and 100 cents per lb. How much of each kind must he take to make a mixture worth 85 cents per lb. ? Ans. 1, 1, 1, 2. Ex. 6. A wine-merchant wishes to mix wine worth $1.20 and $1.40 per gallon, with water. How much of each kind must he use to make a mixture worth $1.00 per gallon? Ex. 7. A goldsmith wishes to combine gold 22 carats fine; 19 carats fine; 18 carats fine; and 17 carats fine. In what proportion must they be united that the compound may be 20 carats fine? Ex. 8. A farmer wishes to mix 60 bushels of corn, at 60 cents a bushel, with rye, at 75 cents; barley, at 50 cents; and oats at 45 cents. What quantity of rye, barley, and oats must be taken that the mixture may be worth 65 cents a bushel ? rye, must be increased in the same ration: i. e., be multiplied by 6. Ex. 8. A grocer wishes to mix 100 pounds of coffee, worth 12 cents, with coffee worth 15, 10, and 8 cents. What quantities must he take that the mixture may be worth 11 cents a pound? 10. A wine-merchant wishes to fill a cask containing 36 gallons with a mixture of wines worth $1.00, $1.20, $1.50, and $1.60 per gallon. How many gallons of each kind must he take that the mixture may be worth $1.40 per gallon? Explanation.-Since, in the first case, the amount required -36 gallons-is of the amount obtained by mixing 20 gallons of the first kind, 10 gallons of the second, 20 gallons of the third, and 40 of the fourth, it is evident that of the quantity of each ingredient must be taken. In the second case, the amount required is 4 times the amount obtained; ៖ and, hence, the quantity of each ingredient must be multiplied by 4. Ex. 11. A trader wishes to fill 10 casks, each containing 28 gallons, with a mixture of brandy, rum, and water. If the brandy is worth 80 cents a gallon, and the rum 95 cents, how many gallons of each must be taken that the mixture may be worth 75 cents ? PARTNERSHIP. ART. 161. Partnership is the association of two or more persons, for the purpose of carrying on business at their joint expense. Each person thus associated is called a partner; and the several partners, in their associated capacity, are called a company, firm, or house. The money or property invested by such a company in business is called their capital, or joint-stock, or stock in trade. The profits and losses of the business are sometimes shared by the several partners in proportion to their stock in trade; or more correctly, in proportion to the use or interest of their stock in trade. When the stock of the several partners is invested for the same length of time the interest of the stock is proportioned to the stock itself; and, hence, the profits and losses in this case are shared in proportion to the stock of the several partners. Sometimes one or more of the partners furnish the capital, and the other or others contribute their services. The profit or loss to be shared is called a dividend. The duration of a partnership is limited by contract, or is left indefinite, subject to be dissolved by mutual consent and agreement. When a company is dissolved, either by the limitations of the contract or by mutual agreement, the adjustment of the accounts of the company, and the division of effects, is called a partnership settlement. Note.-Although partnership settlements fall properly within the province of book-keeping, we have added a few examples to illustrate the manner of closing such accounts. ART 162. When the capital of the several partners is invested for the same length of time, to find each partner's share of the profit or loss. Ex. 1. A, B, and C enter into partnership in the lumber business for 3 years. A put in $2400; B, 3600; C, $600. At the time of the dissolution of the firm the net profits were $4000. What is each partner's share of the profits? FIRST METHOD. A's stock, $2400% of entire stock. 3600-3600 12000 ΤΟ of $4000=$ 800 = of $4000-1200 $4000 Explanation.-Since A's stock equals, B's, and C's of the entire stock, A would be entitled to, B to, and C to of the entire profits. Explanation.-Since the entire profits equal of the entire stock, each partner's share of the profits must equal of his stock. |