Maths holiday HW S3 to S4

2015-06-28 11:09 pm

1. In a company, junior workers and senior workers (but not the managers) work as teams. Senior workers form 10 teams while junior workers form 20 teams. The number of junior workers in forming a team is 3 more than the number of senior workers in forming a team It is given that the total number of staff members (including the managers) in the company does not exceed 470.

(a) What is the maximum number of senior workers in forming a team?
(b) It is given that the number of senior workers in forming a team is not less than 12. Is it possible that there are more than 50 managers in the company? Explain youe answer.

2.Express 27 x 16^11 + 16^7 + 33 x 16^4 - 16^4 as a hexadecimal number.

回答 (1)

Tracy

2015-06-29 1:25 am

✔ 最佳答案

1.
(a) Let number of junior workers be x, senior workers be y. Asume there is only one manager(min.).
x/20 = y/10 +3 ---- (1)
x+y+1 < 470 ---- (2)

(1): x = 2y + 60 ---- (3)
Sub. (3) into (2)
2y + 60 + y + 1 < 470
y < 136.333...
Senior workers can be devided into 10 groups,
Therefore Max. number of senior workers is 130.

(b) If there are 130 senior workers,
there will be (13/10 + 3)*20 = 320 junior workers.
There can only be 469 - 130 - 320 = 19 managers.
Therefore it is not possible.

2. 27 x 16^11 + 16^7 + 33 x 16^4 - 16^4
= 27 x 16^11 + 16^7 + 32 x 16^4

Short devision:
16 L27
16 L1 ... 11(B)
0 ... 1
So 27(10) = 1B(16)

16 L32
16 L2 ... 0
0 ... 2
So 32(10) = 20(16)

Therefore ans = 1B00010200000

https://www.youtube.com/watch?v=QgVc1Tl-JDA
(This may help you understand)

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