Section XLIV. MISCELLANEOUS EXAMPLES. 118. 1. A can do a piece of work in 2 days, and B can do the same work in 3 days; what part of the work can A do in 1 day? what part of it can B do in 1 day? 2. If A can do of a piece of work in 1 day, and B can do of it, what part of the work can both together do in 1 day? How long will it take both together to do the whole work? 3. Mr. Jones can cut a lot of wood in 2 days, and his son can cut the same lot in 4 days; what part of the lot can both together cut in 1 day? In how many days can both together cut the lot? 4. A cistern has 2 outlets: by one it can be emptied in 3 minutes, and by the other in 5 minutes; in how many minutes can both together empty it? 5. A can reap a field in 3 days, and B can reap it in 4 days; in what time can both together reap it? 6. A quantity of earth can be removed by men in 12 days, by horses in 4 days, and by a steam engine in 2 days; in what time can it be removed by all together? 7. A can dig of a trench in 4 days, and B can dig of it in 2 days; how long would it take for A to dig the whole? for B? How many days would it take both together to dig the whole? 8. If John can eat of a barrel of apples in 2 weeks, and Rollo can eat of a barrel in 5 weeks, in what time can both eat 1 barrel? 9. If 1 pound of tea will last a man and his wife together 2 weeks, and if it will last the man alone 6 weeks, how long would it last the woman alone? NOTE. The woman drinks —, which is of the tea, in 1 week. 10. Mary and Ellen together can do the washing for a certain family in 4 hours: if Ellen can do it alone in 6 hours, in what time can Mary do it alone? 11. Lyman can make a case of boots in of a month, and Walter can do the same work in of a month; how many cases can both make in 1 month? How long would it take both together to make 1 case? 12. A can do a piece of work in of a day, and B can do the same work in of a day; how long would it take both to do it? 119. 1. A pencil and a pen together cost 9 cents: if the pencil costs twice as much as the pen, what does each cost? Solution. 9 cents equals the cost of the pen plus twice the cost of it, which is 3 times the cost of it; hence, of 9 cents or 3 cents is the cost of the pen, and 3 of 9 cents or 6 cents is the cost of the pencil. 2. A man sold a cane and a knife for 8 dollars: for the cane he received 3 times as much as for the knife; what did he receive for each? 3. What number added to twice itself gives 21? 4. The sum of the ages of a brother and sister is 24 years, and the brother is 3 times as old as the sister; how old is each? 5. A and B receive $20 for mowing a field; if A receives 4 times as much as B, what part of the money does each receive? 6. Divide $24 among A, B, and C, so that B shall have 2 times as much as A, and C shall have as much as both A and B. 7. A man dying, left $50,000, as follows: to each of his two nephews a certain sum, to his son 4 times as much as to each of his nephews, and to his wife $2000 more than to his son and nephews together; how much did he leave to each? 120. 1. There are 26 fowls in a yard: 2 more than one half of them are hens, and the rest turkeys; how many are turkeys? 2. A man sold a chair for $14.75, which was $2.25 more than double what it cost him; what did it cost? 3. A book and a map together, cost $5; if the book cost $1 more than the map, what did each cost? NOTE. If $1 is taken out of $5, the remainder will equal the cost of two books. 4. Upon a certain tree there are 3 more sparrows than robins, and there are 15 birds of both kinds; how many are there of each? 5. A certain class consisted of an equal number of girls and boys; if, after 4 boys had left, 18 pupils remained, how many of each sex were in the class at first? 6. The sum of two numbers is 12, and one of them is 2 more than the other; what are the numbers? 7. The sum of two numbers is 17, and the difference is 3; what are the numbers? 8. In a school of 80 pupils there are three classes : the first and second classes have an equal number of pupils, and the third class has 5 more than the first or second; how many are there in each class? 9. The profits on a book are 45 cents; how can this sum be divided so that the publisher shall have 4 times as much as the author, and the retailer shall have 5 cents more than the author and publisher together? 121. 1. What number is that to which if of itself is added, the sum is 66? [See Art. 84, Example 23.] 2. Divide the number 10 into two such parts that the less shall be as large as the greater. 3. Divide 16 apples between Albert and Mary, giving to Mary as many as to Albert; how many apples will each have? 4. How shall A and B divide $30 between themselves so that B shall have as many dollars as A? 5. A steamer and a locomotive start from a landing at the same time and go in opposite directions; if the steamer goes as fast as the locomotive, as fast as the locomotive, how many miles will each have gone when they are 48 miles apart? 6. The top of a tree 64 feet high was broken off in a storm if the part broken off was equal to of the part standing, what was the length of each part? 7. Divide 1 hour (60 minutes) into two such parts that of the greater part shall equal the less; what are the parts? 8. Divide 28 into two such parts that the second part shall contain more than the other part. Suggestion. 28 contains the first part plus of the first part, or of it. 9. Jane and Mary divided some cambric between themselves, so that Jane had more than Mary; what part of the cambric did each have? 10. Mr. Mason sold a gold pencil and a pen for $22 ; if the price of the pencil was 20 per cent. higher than the price of the pen, what was the price of each? 122. 1. Charles bought an equal number of 2-cent stamps and 3-cent stamps, paying for the whole 15 cents; how many of each kind did he buy? Solution. For 1 of each kind he would pay 5 cents; hence, for 15 cents he could buy as many of each kind as there are 5's in 15; there are three 5's in 15; therefore, etc. 2. A tailor had 36 yards of cloth, which he wished to cut so as to have an equal number of coats and vests, the coats to contain 6 yards each, and the vests 21 yards each; how many of each could he have? 3. A grocer mixes two kinds of sugar in equal quan tities, one of which cost 6 cents a pound and the other 5 cents a pound; he sells the mixture for $1.10, and thereby makes 11 cents; how many pounds of each kind of sugar did the mixture contain? 4. A trader has apples which he sells, some for $2 a barrel, some for $3, and some for $4 a barrel; if he sells an equal number of each kind, and receives $72 for the lot, how many of each kind does he sell? 5. A druggist receives an order for an equal quantity of each of three kinds of drugs, one kind being worth $3 another worth $11, and the other worth $2 a pound: if he receives $50 for the whole, how many pounds of each kind are required to fill the order? 6. A shoe dealer fills an order for $70 worth of boots, one kind worth $4 a pair, another worth $3 a pair: of the latter kind there are twice as many pairs as of the former; how many pairs of each kind are required? 7. A confectioner bought glass jars, some at $15, and some at $23 apiece, of the former kind 4 times as many as of the latter; if he paid $60 for the lot, how many of each kind did he buy? 123. 1. What is the ratio of 2 to 3; that is, 2 is what part of 3? NOTE. Ratio means relation. In expressing the relation of two numbers, we express what part one number is of another, or how many numbers equal to one number there are in another; thus, the ratio of 2 to 4 is ; that is, 2 is of +; the ratio of 4 to 2 is 2; that is, 4 is two 2's. 2. What is the ratio of 3 to 6? of 6 to 3? of 3 to 4? 3. The ages of two boys are in the ratio of 3 to 4 : the age of the younger is 12 years; what is the age of the elder? NOTE. The ratio of 3 to 4 is ; hence, 12 years is of the age of the elder boy. 4. Two numbers are in the ratio of 5 to 2; if the larger number is 20, what is the smaller number? |