and would weigh 14 lb. and cost 25 cents per pound. Which would be the cheaper and how much? 59. I want to measure out 21 gallons of water, but I have no measure at hand. However, there are some scales handy and I proceed to weigh out the proper amount in a pail that weighs 17 lb. What should be the total weight of the pail and the water, if one gallon of water weighs 8 lb.? 60. I want to cut 300 pieces of steel, each 112 in. long for wagon tires. I have in stock a sufficient number of bars of the same size, but they are 120 in. long; and I also have a sufficient number 235 in. long. Which length should I use in order to waste the least material? Calculate the total number of inches of stock that would be wasted in each case. CHAPTER IV MONEY AND WAGES 27. U. S. Money.-Nearly every country has a money system of its own. The unit of money in the United States is the dollar. To represent parts of a dollar, we use the cent, which is of a dollar. Fifty cents is 10% of a dollar; it is also one-half dollar (5%). Likewise, twenty-five cents is 25 dollar, or one-quarter dollar. 50 In writing United States money, the dollar sign ($) is written before the number; a period called the decimal point, is placed after the number of dollars; following this decimal point is placed the number of cents. Two dollars and seventy cents is written $ 2.70 $ 15.07 $125.00 $ 1.25 $ .35 $ .08 Since one cent is 1 dollar, it follows that the figures to the right of the decimal point represent a fraction of a dollar. These figures are the numerator, and the denominator is 100. The first figure following the decimal point can be said to indicate the number of dimes, because 1 dime = 10 cents, and this figure indicates the number of tens of cents. Also this number represents tenths of a dollar, because 1 dime = 10 cents =10% dollar = dollar. The second figure after the decimal point indicates cents, or hundredths of a dollar. This decimal system of writing amounts of money has great advantages in performing the operations of addition, subtraction, multiplication, and division, because we can perform these operations just as if we were dealing with whole numbers, which makes the work much simpler than if we had fractions to deal with. 28. Addition. We can add numbers made up of dollars and cents and carry forward just as in simple addition. The number of tens of cents will represent dimes (10 cents=1 dime; 30 cents =3 dimes, etc.) and thus can be carried forward and added into the dime column. Likewise, the number of tens of dimes will represent dollars (10 dimes = 1 dollar) and, therefore, this number can be added into the dollar column. Example: Add $5.20, $2.65, $3.25, and $.35. $5.20 $11.45, Answer. Explanation: Adding the cents column, we get 5+5+5+0=15 cents. Put down the 5 and crary the 1 into the next column (since 15 cents = 1 dime and 5 cents.) Adding the dimes, we get 1+3+ 2+6+2 14 dimes. Put down the 4 and carry the 1 into the dollar column (since 14 dimes = $1.4). 1+3+2+5=11 dollars, which we put down complete. The decimal point we now place in the sum exactly as it was in the numbers added, so that it properly separates dollars from cents. The only precaution to be observed is to see that the dollars, dimes, and cents are properly lined up vertically before adding. To do this it is only necessary to see that the decimal points are kept in a straight vertical line. Example: What is the total cost of three articles priced as follows: $2.25, $1, and $1.75? $2.25 1.75 $5.00, Answer. Explanation: Here the $1 does not have any decimal point or cents after it, and care should be taken to see that it is put down in the dollar column and not in the cents column. $1 can be written $1.00, if desired, to avoid any danger of a mistake. 29. Subtraction.—The same rules should be followed in subtracting. If any figure in the subtrahend is larger than the corresponding figure in the minuend, we can borrow 1 from the figure next to the left, just as in ordinary subtraction. Example: A man draws $24.75 on pay day and immediately pays bills amounting to $8.86. How much does he have left to put in the bank? $24.75 $15.89, Answer. Explanation: Having set down the numbers properly, we subtract just as if we were subtracting whole numbers. The only difference is that, after subtracting, we put the decimal point in the remainder directly below the other decimal points, to separate the dollars and cents in the remainder. 30. Multiplication.—In multiplying an amount of money by any number, the process is the same as in simple multiplication, remembering, however, to keep the decimal point to separate the dollars from the cents. The reasoning for this is just the same as in addition. Multiplying cents, gives cents; multiplying dimes gives dimes, and multiplying dollars gives dollars. The figures left over are carried forward just as in plain multiplication, because 10 cents=1 dime, and 10 dimes = 1 dollar. Examples: 1. What should a machinist receive for finishing 48 gas engines pistons at 25 cents each? $.25 200 $12.00, Answer. Explanation: The 25 cents is put down as $.25. The multiplication of 25 by 48 is performed as usual. Then the decimal point is placed in the product to separate the dollars and cents by leaving the two places, counting from the right, to repre sent cents. 2. If you owe 2 weeks board at $3.25 a week, how much money will it take to settle the bill? $3.25 1621 $8.12 Answer. Explanation: First, we put down the numbers and then multiply as if we were simply multiplying 325×21. The product is 812, but since we are dealing with dollars and cents, we must put the decimal point in the product to show what part of it represents dollars and what part cents. 31. Division. In dividing an amount of money by any number, the division is carried out as in ordinary division. The decimal point is then placed in the quotient in the same position (from the right) that it had in the dividend. Example: The weekly pay roll of a company employing 405 men is $4880.25. What is the average amount paid to each man? Another way of locating the decimal point is to place it in the quotient as soon as the number of dollars in the dividend has been divided. Taking the same example; we first divide 405 into 488 and get 1, with a remainder of 83. Annexing the next figure 0 and dividing again, we get 2 for the quotient. We have now divided the number of whole dollars (4880) and have $12 for the quotient, with a remainder of 20. The 12 is, therefore, the number of whole dollars in the quotient. We now bring down the next figure (2) from the dividend and find that 405 will not go into 202, so we have 0 dimes. Then, bringing down the five cents, we get 2025 cents, which, divided by 405, gives just 5 cents. The men, therefore, get an average of $12.05 each, per week. 32. Reducing Dollars to Cents.-Sometimes we find it desirable to change a number of dollars and cents all into cents. To do this, merely remove the decimal point from between the dollars and cents and you will have the number of cents. Every one knows that: $1.00 is 100 cents $1.25 is 125 cents $.25 is 25 cents Likewise: $ 12.75 is 1275 cents $1000.00 is 100000 cents What we have really done in making these changes is to multiply the dollars by 100 to get the equivalent cents. We have taken a mixed number and multiplied it by 100 because there are 100 cents in a dollar. This operation is performed by moving the decimal point two figures to the right, or placing it after the cents, where it is, of course, useless and is seldom written. In many problems it is quite desirable to change the dollars to cents and carry the work through as cents. The following example shows clearly such a case. Example: During one month a foundry turned out 312,000 lb. of iron castings. The total cost of the iron used, including the cost of melting and pouring was $3900. What was the cost, in cents, of 1 lb. of iron, melted and poured? $3900 $3900.00 390000 cents. 390000312000=1; 78 1312-1 cents, Answer. = Explanation: Since the cost of iron, melted and poured, is but 1 or 2 cents, we might as well change the total cost to cents before we divide by the number of pounds. Then we will get the cost directly in cents per pound, as we want it. 33. Reducing Cents to Dollars.-The reduction of cents to dollars is really performed by dividing the number of cents by 100, since there are 100 cents in 1 dollar. This shows us that the following simple rule can be adopted for this reduction: To reduce cents to dollars, place a decimal point in the number so as to have two figures to the right of the decimal point. 34. The Mill.-There is another division of U. S. money called the mill. A Mill is one-tenth of a cent or one one-thousandth of a dollar. 100 mills = 10 cents=1 dime 1000 mills=100 cents = 10 dimes = 1 dollar There is no coin smaller than the cent and, therefore, the mill is merely a name applied in calculations where it is desirable. to have some unit smaller than the cent. For example, tax rates are usually given in mills per dollar. A tax rate of 15 mills on the dollar would mean that a person would have to pay 15 mills (or 1 cents) on each dollar of assessed valuation. Cost accountants generally figure costs down as fine as mills and even, in some cases, to tenths of mills or finer. |