EXERCISE 91 Example 1. Find the weight in pounds Avoirdupois of 5000 silver dollars. A silver dollar weighs 412 grains. SOLUTION. 1 lb. (Troy) = 5760 grains. 1 lb. (Avoirdupois) = 7000 grains. 1 dollar weighs 412 grains. 5000 dollars weigh 5000 x 412 grains. 5000 dollars weigh as many pounds as the number of times that 7000 grains are contained in 5000 x 412 grains. 5000 × 412-294 lb. Av. 7000 2. Find the weight in pounds Troy of 1,000,000 silver dollars. Find also the weight in pounds Avoirdupois. 3. A silver dollar is 90% silver. Find the weight of pure silver in one silver dollar. 4. The commercial value of a silver dollar is the value of the pure silver it contains. What is the commercial value of a silver dollar when pure silver is worth 66¢ per oz. (Troy oz.)? 5. A 10-dollar gold piece weighs 258 grains. Find the weight of 10,000 dollars in gold. Find also the weight of 1,000,000 dollars in gold. 6. Gold coins contain 90 % pure gold. Find the weight of pure gold in a 10-dollar gold piece. 7. The alloy in a gold coin neither adds to nor takes from the value of the coin. Compute the value of 480 grains of pure gold. (Remember that 90% of 258 gr. is gold worth $10.) 8. The bullion value of the pure silver in a silver dollar at the average price of silver for the year 1905 was $.472. Find the value of 1 oz. Troy of pure silver. 9. In 1906 the value of an ounce of pure silver was $.6769, and the value of an ounce of pure gold was $20.67. How many ounces of silver could be bought for one ounce of gold at those prices? SOLUTIONS OF PROBLEMS THE UNIT METHOD Example 1. If 17 bu. of wheat cost $15.30, find the cost of 15 bu. Example 2. If 25 men do a piece of work in 18 days, how long will it take 20 men to do the same work? SOLUTION. 25 men take 18 da. to do the work. .. 1 man takes 18 da. × 25 to do the work. EXERCISE 92 1. If 19 bu. of wheat cost $14.25, find the price of 11 bu. of wheat. 2. Seven men can dig a trench in 16 da. will it take 10 men to do the same work? How long 3. If 11 sheep cost $71.50, find the cost of 17 sheep at the same rate. 4. If 14 men can do a piece of work in 11 da., how long will it take 21 men to do the same work? 5. The earth revolves on its axis 15° in 1 hour. Through how many degrees does it revolve in 23 minutes? 6. Twelve horses plow a field of 47 acres in 7 days. How many acres will 8 horses plow in the same time? 7. A pole 30 ft. high casts a shadow 24 ft. long. Find the length of the shadow cast by a pole 70 ft. high. 8. How long will it take 20 men to pave a street which 15 men pave in 15 days? 9. A sum of money yields $40.30 interest in 125 days. What interest will the same sum yield in 75 days? 10. A train runs 40 miles in 1 hr. and 20 min. How far will it run in 2 hr. ? 11. If 3 acres of land are worth $ 259, what is the value of 2 acres? 12. If of an acre of land is worth $89, how much is a tract measuring 21 acres worth? 13. A train runs 45 miles an hour. feet it will go in 1 minute; in 1 second. Find how many 14. When the rate of a train is 36 miles an hour, what is its rate in feet per second? 15. Sound travels 1 mile in 5 seconds. How long will it take sound to travel 4400 feet? 16. Light travels from the sun to the earth, a distance of 92,790,000 miles, in 8 minutes and 18 seconds. Find its rate per second. 17. If of a clerk's yearly salary is $900, what is his salary per month? 18. If 11 yards of carpet can be bought for a certain sum of money, how many yards can be bought for the same sum when the price of carpet falls 8%? MISCELLANEOUS TOPICS WORK AND TIME Example 1. A can do a piece of work in 6 da., and B can do the same piece of work in 8 da. In what time can A and B do the work together? ANALYTICAL SOLUTION. A does of the work in 1 da. B does of the work in 1 da. A and B together do (+) of the work in 1 da. of the work in 1 da. A and B do A and B do of the work in of 1 da. A and B do 24 of the work in 24 of 1 da. .. A and B do the work in 3 da. Example 2. A cistern has three pipes. The first pipe fills the cistern in 12 hr., the second, in 15 hr., and the third empties it in 10 hr. In what time will the cistern be filled, if all three pipes run together, and the cistern is empty when the pipes start running? ANALYTICAL SOLUTION. The first pipe fills of the cistern in 1 hr. The second pipe fills of the cistern in 1 hr. The third pipe empties of the cistern in one hour. The first two pipes would fill (2+) of the cistern in 1 hr. +2% • 3 But during each hour an amount equal to of the capacity of the cistern runs out through the third pipe. So the amount left is the difference between what runs in during the hour and what runs out. This is which equals 2. 20 the three pipes fill of the cistern in 1 hr. the three pipes fill 20 of the cistern in 20 hr. .. the cistern is filled in 20 hr. Example 3. A and B do a piece of work in 31 hr.; A alone, in 7 hr. In what time does B do the work? 1 SOLUTION. A and B together do of the work in 1 311 hr.; i.e. A and B together do of the work in 1 hr. B alone does (-) of the work in 1 hr. .. B does the work in 8 hr. Example 4. A and B can mow a field in 21 hr. A can do as much work as B. Find the time in which each does the work. SOLUTION. Represent B's work by the rectangle mnst. Divide it into four equal parts. Then A's work is equal to three of these parts. Represent A's work by the rectangle pqxy formed of three parts equal to the parts in rectangle mnst. Then the two rectangles together represent as much as the whole field. If it takes A 21 hrs. to mow three of the parts, or of the field, it will take him of 21 hrs., or 7 hrs., to mow one part, or of the field. If it takes him 7 hrs. to mow one part, or of the field, it would take him 7 x 7 hrs., or 49 hrs., m S to mow the seven parts, or of the field, which is the whole field. Similarly, if it takes B 21 hrs. to mow 4 parts, or of the field, it will take him 21 hrs. to mow of the field, |