EXAMPLE: 43 hr. @ $25.00 per week on a 48-hr. basis 48 of $25.00 = $1075; $22.40 48) $1075.00 Ans., $22.40 = ? When the use of aliquot parts is impossible, find the proper fractional part of the rate per week, but always multiply by the numerator before you divide by the denominator because you will usually have to multiply a difficult fraction if you first divide by the denominator to find the rate per hour and then multiply by the numerator. EXAMPLE: 422 hr. @ $27.00 per week on a 48-hr. basis X 1 16 or $24.05, Ans. multiplying both terms of the fraction by 4 and continue as before, or clear by using decimals. Examine this and state which is the shortest way. Exercise 29—Oral. 1. If a carpenter is paid on the basis of 45 hr. per week, what fraction of a week's wages does he receive for 1 hour's work? 2. A machinist is paid on the basis of 48 hr. per week what fraction of a week's wages does he receive for 23 hours' work? 3. An electrician is paid on the basis of 42 hours per week; what fraction of a week's wages does he receive for 392 hours' work? 4. At the rate of $32.00 for 48 hours' work, how would you find the amount of wages to be paid to a bricklayer for working 8 hours? 5. A teamster who is paid on the basis of $24.00 for 52 hours' work per week, worked 47 hours; how would you find the amount due him? 6. When aliquot parts cannot be used, why is it easier to multiply by the numerator first and then divide by the denominator, than it is to divide first to find the rate per hour and then multiply to find the amount for a certain number of hours? 7. What aliquot part of 48 hours is 6 hours? 8 hours? 12 hours? 16 hours? 24 hours? 8. What aliquot part of 42 hours is 6 hours? 7 hours? 14 hours? 21 hours? 9. What aliquot part of 45 hours is 9 hours? 15 hours? 18 hours? 27 hours? 30 hours? 36 hours? 10. When the number of hours worked is an aliquot part of the number of hours per week, what is the easiest way of finding the amount of wages to be paid? 11. How can you find the wages for 9 hours on the basis of 48 hours per week, using aliquot parts? How for 7 hours? 12. How can you find the wages for 10 hours on the basis of 48 hours per week? For 13 hours? 1. In Department "A" the men are paid on the basis of 48 hr. per week; how much money would be paid to each of the following men: Adams worked 45 hr. @ $18.00 per week. 2. In Department "B" the men are paid on a 48-hr. basis; how much money did he pay to each of the following workers: Bailey worked 8 hr. @ $21.00 per week. 3. In Department "C" where the men are paid on a 45-hr. basis, what would be the total amount of the following pay roll: 2 men worked 45 hr. each @ $30.00 per week. 4 men worked 45 hr. each @ $18.00 per week. 3 men worked 42 hr. each @ $15.00 per week. 6 men worked 30 hr. each @ $21.00 per week. 5 men worked 30 hr. each @ $24.00 per week. 4. S. Smith works in one of the departments where the working hours are from 8.00 to 12.00 o'clock A. M. and from 12.30 to 5.00 o'clock P. M. from Monday to Friday inclusive, and from 8.00 A. M. to 1.30 P. M. on Saturday (without a stop for lunch); how much would Smith receive for working 36 hr. @ $24.00 per week? 5. J. Brown went to work at $8.00 per week in the shop where the working hours are from 8.30 to 12.00 A. M. and from 1.00 to 5.00 P. M. from Monday to Friday inclusive, and from 8.30 A. M. to 1.00 P. M. on Saturday; how much would he receive for working full time from Monday morning to Friday night? 6. At the rate of $24.00 for 48 hours' work, how many hours must James Fitzgerald work to receive $20.00? 7. At the rate of $33.00 for 45 hours' work, how many hours must Samuel Jones work to receive $27.50? 8. If Tom Daly is paid $15.00 for working 20 hours, how much would he receive for working a full week consisting of 48 hours? 9. At what rate of wages for a week of 48 hours must Wm. Beach work to receive $7.50 for 18 hours' work? LESSON 15 Transposition in Figuring Wages EXAMPLE: 71 hr. @ $12.00 per week on a 48-hr. basis = ? We can "transpose or change the order of the numerators in an example in cancellation without affecting the result, as is very readily proven. By using this simple device in figuring wages, much time and work can be saved. Is 2 X 4 the same as 4 X 2? Is 10 X 12 the same as 12 X 10? Supposing we wanted to find the amount of wages to be paid for 37 hours' work at $16.00 per week on a basis of 48 hours per week; if we transpose the hours worked and the rate per week, the example would read: 16 hours @ $37.25 per week on a 48-hour basis, and could be worked very easily by aliquot parts as follows: 1148 week; of $37.25 = $12.42, which is the answer. We chose 18 because 16 is an aliquot part of Watch for the relation of one number to another. 48. = Therefore, when the rate per week is an aliquot part of the weekly hour basis, call the hours "dollars" and the dollars "hours" and work as usual. In this way, wages for almost any number of hours at $6.00, $8.00, $12.00, etc., per week on a 48-hour basis can be figured by the use of aliquot parts without using paper. |