(2) Divide $248 into parts proportional to the fractions, 15, 25. Multiply the fractions by 150, the L. C. M. of their denominators. The results are 15, 10, 6. Hence, the parts will be represented by the numbers 15, 10, 6, and the whole by 31. Therefore, the respective parts will be }, }, That is, $120, $80, $48. Ans. EXERCISE LXV. of $248. 1. Divide $12,000 proportionally to the numbers 3, 4, 5. 2. Divide 815 tons proportionally to 1, 4, 1, . 3. Divide 6853 lbs. of wool proportionally to 14, 24, 58; and also proportionally to the reciprocals of these numbers. 4. Two persons join in purchasing some property, one paying $1250 and the other $1000. If the property rise in value to $3600, what will be the value of each one's share? 5. Gun-metal is composed of 3 parts (by weight) of tin to 100 parts of copper. What weight of each of these metals will there be in cannon weighing 721 lbs.? 6. Bell-metal contains 78 parts copper and 22 parts tin. What weight of each of these metals will there be in a bell weighing 937 lbs. ? 7. It takes 75k of saltpeter, 12.5kg of charcoal, and 12.5kg of sulphur to make 100kg of powder. How much of each of these substances will be required to make 10,000,000 cartridges, each containing 5o of powder? 8. Yellow copper contains 2 parts of red copper and 1 part zinc. How many ounces of red copper are there in an article weighing 1 lb. made of yellow copper? 9. Type-metal is made of an alloy containing 39 parts of lead to 11 parts antimony. How many pounds of each will be required to make 957 lbs. of type? 10. Plumber's solder contains 2 parts lead and 1 part tin. How much of each of these in 100 lbs. of solder? 11. The air is composed of oxygen and nitrogen. In 100 volumes of air there are 21 volumes of oxygen and 79 of nitrogen. Reckoning the weight of a liter of oxygen to be 1.42958, that of a liter of nitrogen 1.25776, find the number of grams of each gas in 100% of air. 12. What is the value of the gold in a chain weighing 3 oz. 4 dwt., supposing it to be 18 carats fine (that is, 18 parts of pure gold out of 24), at $19 an ounce? PARTNERSHIP. 342. Partnership is separated into simple and compound. In simple partnership the capital of each partner is invested for the same time. In compound partnership the time for which the capital of each partner is invested is taken into account, as well as the amount of the capital; and the division of profits and losses is made proportionally to the amount of the capital and the time it is invested. EXERCISE LXVI. 1. Arnold and Baker enter into partnership. Arnold puts in $6000 for 8 months, and Baker $4000 for 6 months. Their profits are $2000. What is each man's share? NOTE. Since the use of $6000 for 8 months is equivalent to the use of $48,000 for 1 month; and the use of $4000 for 6 months is equivalent to the use of $24,000 for 1 month, their profits must be divided in the ratio 48,000: 24,000. 2. Dobson furnishes the firm of Dobson & Fogg with $5000 for 13 months; Fogg furnishes $7000 for 9 months. Their profits are $1700. What is the share of each ? 3. In a business speculation, A furnishes $800, and after 3 months $250 more; B furnishes $950, and at the At the end end of 2 months withdraws $200; C furnishes $650, How shall 4. Two partners, A and B, begin business with capitals of $3500 and $8700, and A is to have .12 of the profits for managing the business. How shall a profit of $1906.25 be divided between them? 5. A puts $2100 into a business, and B $1750. At the end of a year each puts in $700 more, and C joins them with $2500. At the end of 18 months from this time how shall a profit of $2166.50 be divided? 6. Three graziers hire a pasture, for which they pay $132.50. One puts in 10 oxen for 3 months, another 12 oxen for 4 months, and the third 14 oxen for 2 months. How much of the rent ought each to pay? 7. A begins business, with a capital of $2400, on the 19th of March; and on the 17th of July admits B as a partner, with a capital of $1800. Dec. 31 the profits are $943. What is the share of each? 8. A and B join capitals in the ratio 7:11. At the end of 7 months A withdraws of his, and B of his; and, after 11 months more, they divide a profit of $5148.50. What is the share of each? 9. Divide £65 9s. among three persons, so that the first have as many half-crowns as the second has shillings; and the second as many guineas as the third may has pounds. 10. Two partners begin business each with a capital of $2000. A adds $500 at the end of 2 months, and $500 more at the end of 7 months; B adds $800 at the end of 3 months. What is the share of each, at the year's end, of a profit of $3605.25? CHAPTER XVI. PERCENTAGE. 343. In considering the increase or decrease in quantities, it is usual to employ, as a common standard of reference, the number 100. Thus, if the population of a town at one census were 1200, and at the next 1500, the increase would be 300 in 1200; that is, 25 in every 100; or, as it is generally expressed, 25 per cent. 344. The symbol % is used for the words per cent. 345. The representative number resulting after an increase has taken place will be 100+ increase per cent; and after a decrease has taken place will be 100 decrease per cent. 346. The representative numbers in any particular case may be changed to quantities by applying them all to the same unit of quantity. Thus, if gunpowder be said to contain 75% of saltpetre, the meaning is, that if the number 100 be taken as the representative of the whole weight, the number 75 will represent the weight of saltpetre in it; and if the numbers be applied to any unit of weight, as a pound, the meaning will be, that 100 lbs. of gunpowder will contain 75 lbs. of saltpetre. (1) Ten years ago the population of a city was 26,275, and has increased 20%. What is its present population? If 100 be taken to represent the population ten years ago, 100+20 will represent the present population. Therefore, the present population will be 18 of 26,275 = 31,530. Ans. = (2) Ten years ago the population of a city was 26,275; its present population is 31,530. Determine the increase per cent. 31,530-26,275=5255, actual increase. Since the increase on 26,275 is 5255, the increase on 100 is 215 of 5255 = 20. The increase, therefore, is 20%. Ans. (3) A town, after decreasing 11%, has 4539 inhabitants. Find its number at first. If 100 be taken to represent the population at first, 100–11 = 89, will represent the present population. = Therefore, the population at first was 100 of 4539 = 5100. Ans. (4) In a certain school there are 200 girls, and the girls are 40% of the whole number of pupils. many pupils in the school? How If 100 be taken to represent the whole number of pupils, 40 will represent the number of girls. Therefore, the whole number of pupils is 100 of 200-500. Ans. (5) 50 lbs. is what per cent of 450 lbs.? If 100 be taken to represent the whole weight, the number required to represent 50 lbs. will be of 100 = 11}. That is, 113% Ans. 347. In the process of computing by the hundred, it is generally more convenient to use 1 as the representative number, and to express the per cent as hundredths. Thus, in example (1), if the number 1 be taken to represent 26,275 inhabitants, 1.20 will represent the number of inhabitants after an increase of 20%; and the present population will be 1.20 of 26,275 → 31,530. Ans. |