Exercise 137 1. Divide $1250 into parts proportional to 3 and 2. 2. Divide 500 into parts proportional to 2, 3, and 5. 3. The sum of 2 numbers is 480, and the larger is to the smaller as 9 is to 7. What are the numbers? 4. The difference of two numbers is 50, and the larger is to the smaller as 6 is to 5. What are the numbers? 5. A and B together invested $ 225. A invested $7 as often as B invested $3. How much did each invest? 6. Divide 20 into parts proportional to and. SUGGESTION. 1st part 2d part=1:1 = 3:2. 7. Solder for lead consists of 1 part tin to 1 parts lead; how much of each of these substances is necessary to make 5 lb. of solder? 8. A, B, and C are charged $36 freight on a shipment of potatoes, of which A shipped 200 bu., B, 300 bu., and C, 500 bu.; how much should each pay? 9. Three men received $62.50 for husking a field of corn; the first husked 300 shocks, the second 450 shocks, and the third 500 shocks; how much should each receive? 10. After ducklings are 10 days old, a good feed for them consists of the following parts by weight: 3 parts bean 1 part corn meal 11 parts beef scrap How many pounds of each ingredient are there in 360 lb. of this mixture? PARTNERSHIP 416. A partnership is an association of individuals, called partners, for the transaction of business. NOTE. A partnership is sometimes called a firm. 417. The capital stock is the amount which the partners invest in the business. NOTE. The assets of a firm are all the property belonging to the firm. The liabilities are all the debts of the firm. 418. When the shares of the partners are invested for equal times, gains and losses are distributed among the partners in proportion to their respective shares. 419. When the shares of the partners are invested for unequal times, gains and losses are distributed among the partners in proportion to their respective shares and times, except when by special agreement some other plan is adopted. Illustrative Examples 1. A, B, and C form a partnership, A investing $600, B $ 800, and C $1000. Divide a gain of $300 among them. The gain is distributed in proportion to the investments. 2. Three boys invested their savings in a news stand; A invested $50 Jan. 1, B $30 Mar. 1, and C $20 Aug. 1. At the end of the year they had a profit of $80 to divide among them; find each one's share. Explanation: A's capital was invested 12 mo., B's 10 mo., and C's 5 mo. the gain on $50 for 12 mo., or the gain on $ 600 for 1 mo. = the gain on $30 for 10 mʊ., or the gain on $300 for 1 mo. = the gain on $20 for 5 mo., or the gain on $100 for 1 mo. A's gain = 1. Three men invested jointly $3000 in a creamery. At the end of the first year their gains were $1500. The first invested $800, the second $1000, and the third $1200; find each one's share of the profit. 2. A and B in partnership gain in 1 year $8560. A contributes $ 8000 and B $7000. A is to retain 25% of the profits for managing the business; how much of the balance should each receive? 3. A merchant failing in business has property to the value of $3200. He owes A $4500, B $2500, and C $2000; how much should each receive? 4. A, B, and C established a coal yard, A furnishing $5000, and B $4000. C's gain for the first year was $198. Find C's capital and A's and B's gain, if the total capital was $18,900. 5. A and B formed a partnership, A putting in $600 for 18 months, and B $800 for a year. They gained $510; what was each partner's share of the gain? 6. A, B, and C formed a partnership. A invested $ 500 on Jan. 1, B $400 on Mar. 1, and C $300 on July 1. At the end of the year they had gained $ 555; what was each partner's share of the gain? 7. A, B, and C take the contract for building a public road. A furnishes 12 men for 60 days, B 20 men for 40 days, and C 10 men for 8 days. They receive for the work $4200, of which A is paid $200 for supervising the work; how much of the balance should each of the men receive? SUGGESTION. The work of 12 men for 60 days equals the work of 720 men for 1 day. 8. A, B, and C contracted to do a piece of work. A sent 24 men for 45 da., B 40 men for 25 da., and C 35 men for 42 da. If the sum paid for doing the work was $ 10,650, find each partner's share. 9. A, B, and C invested jointly $3000. A's capital was invested 12 mo., and his gain was $ 144; B's capital was invested 8 mo., and his gain was $144; C's capital was invested 6 mo., and his gain was $180. Find the capital of each. POWERS, SQUARE ROOT, AND MENSURATION POWERS 420. The square of a number is the result of using the number twice as a factor. Thus, the square of 2 equals 2 × 2, or 4; the square of equals × 1, or 1; the square of .3 equals .3 × .3, or .09. 421. The cube of a number is the result of using the number three times as a factor. Thus, the cube of .5 equals .5 × .5 × .5, or .125. 422. A small figure called an exponent, written to the right and above a number, denotes how many times the number is to be used as a factor. Thus, 72, read 7 squared, equals 7 x 7, or 49; and 73, read 7 cubed, equals 7 x 7 x 7, or 343. Exercise 139 1. Name the square of each number from 1 to 12. 2. Name the square of each of the nine tens. 3. Name the square of each of the nine hundreds. 4. Name the cube of each number from 1 to 5 inclusive. 5. Name the square and also the cube of ;;; }; .2; .3; .5; ; ; .1; .01; .001. ;言; |