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 Likewise: $.25 is 25 cents $ 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. 78 1 390000÷312000=1312-14 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. In sums of money containing mills, there are three figures following the decimal point. The first and second figures after the decimal point indicate dimes and cents, as before. The third figure indicates mills. $.014 is 1 cent and 4 mills It is also 14 mills (since 1 cent 10 mills). = In multiplying or dividing numbers containing mills, we must place the decimal point in the answer in the same position, that is, three places from the right of the number. Example: If your house and lot were assessed at $2000, and the tax rate was 15 mills on the dollar, what would be the amount of your taxes? 15 mills $.015. $.015 2000 $ 30.000, Answer. Explanation: 15 mills is 1 cent and 5 mills, or $.015. This is the amount you must pay on each dollar of assessed value. For an assessment of $2000, you would pay 2000 times $.015, which is $30. 35. Wage Calculations.-The chief use that shop men have, within the shop, for calculations concerning money is in connection with their time and wages. With some wage systems the calculations of one's earnings is comparatively simple; with others it seems rather complicated until the systems are thoroughly understood. The simplest systems are, of course, the well-known day-rate and piece-rate systems. By the old dayrate system, the men are paid according to the time put in, without any reference to the work accomplished. The rate may be so much per hour, per day, or per week, but the method of calculating is the same, and the time keeper will use exactly the same process in each case. The pay roll calculations consist merely in multiplying the number of units of time which each man has to his credit by his rate per unit of time; hours by rate per hour, or days by rate per day. Examples: 1. A machinist puts in 106 hours at 32 cents per hour. How much money is due him from the company? 106 .32 53 212 318 $34.45, Answer. Explanation: The amount due is the product of 106X32. Since the amount will run into dollars. we write the 32 cents as dollars, $.32. The product is $34.45, which is the amount due. 2. The tool-room foreman gets $6.00 a day and has worked 12 days. What is the amount due him? 12 Explanation: The same process is carried out here except that we have the rate per day times the number of days. The piece-work system, by setting prices for certain pieces of work and paying according to the work done, rewards the man in exact proportion to the work that he does. In this system, an account is kept of the amount of a man's work and his pay is calculated by multiplying the numbers of pieces by the piece rates. Example: The price for assembling a certain sized commutator is 55 cents each. If a man assembles an order of 14 of them, how much does he receive? What will he average per day if he does the job in three days? 55¢=$.55 $ .55×14= $7.70 $7.70 32.56 Amount he receives for the job. There are many other wage systems, too numerous to be all explained here. They all are planned to take into account both the amount of work a man does and the time that he puts in to do it. One of these systems, the Premium System, is so well known and so successful as to warrant brief mention here. In its most common form this system is as follows: The men are all placed on a time rate, usually a rate per hour. A record is kept of every man's time and also of the work done by him. Every job has a standard time (sometimes called "the limit") allowed for its completion. On each job, the man's actual time is recorded and also the limit for the job. The man is paid straight wages for the time put in on the job and, in addition, is paid a premium of usually one-half of the time that he saves below the limit. If it takes a man a longer time than the limit, he is paid full wages for the time he puts in. This system is planned to satisfy both parties by giving the efficient man an increased earning, and by giving the firm a share of the time saved, thus giving them a reduced cost whenever they pay higher wages. Let us take an example to see how one's pay would be figured on this plan. Example: In one day, a man whose rate is 27 cents an hour, does the following premium jobs: the first has a limit of 8 hours and is done in 5 hours; the second has a limit of 5 hours and is done in 3 hours; the third has a limit of 3 hours and is finished in 2 hours. What is his pay for the day? 5+3+2=10 hours, actually put in. 8-5 3 hours saved on the first job. He will get paid for the 10 hours and, in addition, for half of the 6 hours that he saved. Altogether he will be paid for 10+ of 6 = 13 hours. 13× 8.272-$3.571, Answer. 1 2 He gets $3.58 for his 10 hours work and, therefore, makes a premium of 83 cents. Meanwhile, the company gets the work done for $3.58, instead of paying $4.40, which it would have cost if the workman had taken the full limit for the work. PROBLEMS 61. Write in figures the following sums of money: One dollar and twelve cents Two dollars and twenty-five cents Fifteen dollars and thirty-seven and one-half cents 62. Read the following and write them out in words: 63. A young man makes the following purchases: Suit of clothes $25, shoes $3.75, hat $2.25, necktie 50 cents. What is the total cost of his purchases? 64. A certain job calls for four in. by 3 in. machine bolts, two § in. by 1 in. set screws, and two in. by 2 in. cap screws. What would be the total cost of the bolts and screws, if the machine bolts are worth 2 cents each, the set screws 11 cents each, and the cap screws 14 cents each? 65. If you bought a house for $3000 and it was assessed at two-thirds of what it cost you, what taxes would you have to pay if the tax rate was 14 mills on the dollar? 66. How much would a man who is paid $4.25 a day earn in a month of 26 working days? 67. If the piece price for a certain job is 4 cents, how many pieces must a man do in one day to make $5.00? 68. An apprentice and a machinist are working together on a piecework job and they earn $30. They are prorated on the job, which means that the money is divided according to their day-work rates. If the apprentice's rate is 10 cents an hour and the machinist's is 30 cents, what fraction of the money does each get, and how much money would each get? |