The national government procured a total of 1550 test kits for the five regions in the country. If the distribution will be solely based on the total number of PUIS and PUMS combined in the region. How many test kits will each region receive? Assume that the total population of the five regions is 560,506. Regions A B CDE PUIs and PUMS Population (by percent) 10% 15% 20% 30% 25%

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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Answer in Adam's Method

The national government procured a total of 1550 test kits for the five
regions in the country. If the distribution will be solely based on the
total number of PUIs and PUMS combined in the region. How many
test kits will each region receive? Assume that the total population of
the five regions is 560,506.
Regions
A
B
CDE
PUIs and PUMS Population (by
percent)
10%
15%
20%
30%
25%
Transcribed Image Text:The national government procured a total of 1550 test kits for the five regions in the country. If the distribution will be solely based on the total number of PUIs and PUMS combined in the region. How many test kits will each region receive? Assume that the total population of the five regions is 560,506. Regions A B CDE PUIs and PUMS Population (by percent) 10% 15% 20% 30% 25%
ADAM'S METHOD
Problem Set:
Region
A
B
с
D
E
Total
1
Districts
Malaya
Masaya
Makabangon
Makabayan
Total
.
Population
56,056
84,076
112,101
168,152
140,127
560,506
Sample Problem (As a guide to answer prob set)
STEPS
Districts
Malaya
Masaya
Determine how many people each representative should
represent.
o Do this by dividing the total population of all
stated by the total number of representatives
o Answer is called the standard divisor or divisor
2. Divide each state's population by the divisor to determine
how many representative it should have
Population
Makabangon
Makabayan
Total
55,000
30,012
25,758
15,123
125,893
If SQ is 60,000
OSQ (RO)-45
SQ
524.2549
286.0716
245.5229
144.1510
SQL-60
SQU-60
55,000
30,012
Population Quota w/ MSD
25,758
15,123
125,893
PUI and PUI SQ
(in
percentage) Quota)
10%
15%
523.3111
285.5566
20%
Standard Divisor = 125,893/ 1200 = 104.9108
If SQ is 45.0001
oSQL-45
OSQU-46
245.0809
30%
143.8915
25%
100%
C
O
o SQ (RO) - 60
Since our initial allocation is above our total number of
pills then we need to increase our divisor to yield smaller
quota
SQU
525
287
246
145
1203
SQU
524
286
246
Number of Pills
per District
144
1200
Number of Pills
per District by
Adam's Method
Standard Divisor = 125,893/ 1200 = 104.9108
Modified Standard Divisor = 105.10
524
286
246
(Standard
144
Round up all quota. Then add. Since we achieved the
desired the total number of pills, it means our modified
divisor for this problem is 105.10
3.
SQU
(Standard
Quota
Upper)
O
o
Record answer to several decimal places
Answer is called the standard quota or quota
No. of Test
kits by
Adam's plan
Round up all the quotas to the nearest whole number
O
Add the values, which can be called initial
allocation or initial apportionment
4. If the sum of initial allocations is larger than our given.
allocations then modify the divisor by increasing our
standard divisor
O Repeat step 2,3,4 until we can allocate all
representatives properly
SAMPLE PROBLEM
Step 1. Compute the Standard Divisor
Step 2. Compute the Standard Quota or Quota per state (SQ)
Step 3. Compute the Standard Quota Round Up value (SQU) and
its summation
Step 4: If the total of the SQU is the same then it is done. If not
the Standard Divisor is incorrect and there should be a Modified
Standard Divisor (MSD)
MSD must be greater than the Standard Divisor
Step 5: Compute the Standard Quota (with MSD)
Step 6: Compute the Standard Quota Upper (SQU) and its
summation
Step 7: If the total of the SQU is the same then it is done and the
MSD is correct. If not then change the MSD again
Step 8: Decision
A group of chemists was able to create anti-hunger pills. They plan
to give all 1200 pills they created to 4 districts to alleviate hunger
due to bring quarantined caused by the pandemic. If they will base
the division of their pills to the number of the population in each
district, how many pills will each district receive?
Districts
Population
55,000
Malaya
Masaya
Makabangon
Makabayan
30,012
25,758
15,123
125893
1200
524.2549
286.0714
245.5229
144, 1510
Page 4 of 8
104.9108
Transcribed Image Text:ADAM'S METHOD Problem Set: Region A B с D E Total 1 Districts Malaya Masaya Makabangon Makabayan Total . Population 56,056 84,076 112,101 168,152 140,127 560,506 Sample Problem (As a guide to answer prob set) STEPS Districts Malaya Masaya Determine how many people each representative should represent. o Do this by dividing the total population of all stated by the total number of representatives o Answer is called the standard divisor or divisor 2. Divide each state's population by the divisor to determine how many representative it should have Population Makabangon Makabayan Total 55,000 30,012 25,758 15,123 125,893 If SQ is 60,000 OSQ (RO)-45 SQ 524.2549 286.0716 245.5229 144.1510 SQL-60 SQU-60 55,000 30,012 Population Quota w/ MSD 25,758 15,123 125,893 PUI and PUI SQ (in percentage) Quota) 10% 15% 523.3111 285.5566 20% Standard Divisor = 125,893/ 1200 = 104.9108 If SQ is 45.0001 oSQL-45 OSQU-46 245.0809 30% 143.8915 25% 100% C O o SQ (RO) - 60 Since our initial allocation is above our total number of pills then we need to increase our divisor to yield smaller quota SQU 525 287 246 145 1203 SQU 524 286 246 Number of Pills per District 144 1200 Number of Pills per District by Adam's Method Standard Divisor = 125,893/ 1200 = 104.9108 Modified Standard Divisor = 105.10 524 286 246 (Standard 144 Round up all quota. Then add. Since we achieved the desired the total number of pills, it means our modified divisor for this problem is 105.10 3. SQU (Standard Quota Upper) O o Record answer to several decimal places Answer is called the standard quota or quota No. of Test kits by Adam's plan Round up all the quotas to the nearest whole number O Add the values, which can be called initial allocation or initial apportionment 4. If the sum of initial allocations is larger than our given. allocations then modify the divisor by increasing our standard divisor O Repeat step 2,3,4 until we can allocate all representatives properly SAMPLE PROBLEM Step 1. Compute the Standard Divisor Step 2. Compute the Standard Quota or Quota per state (SQ) Step 3. Compute the Standard Quota Round Up value (SQU) and its summation Step 4: If the total of the SQU is the same then it is done. If not the Standard Divisor is incorrect and there should be a Modified Standard Divisor (MSD) MSD must be greater than the Standard Divisor Step 5: Compute the Standard Quota (with MSD) Step 6: Compute the Standard Quota Upper (SQU) and its summation Step 7: If the total of the SQU is the same then it is done and the MSD is correct. If not then change the MSD again Step 8: Decision A group of chemists was able to create anti-hunger pills. They plan to give all 1200 pills they created to 4 districts to alleviate hunger due to bring quarantined caused by the pandemic. If they will base the division of their pills to the number of the population in each district, how many pills will each district receive? Districts Population 55,000 Malaya Masaya Makabangon Makabayan 30,012 25,758 15,123 125893 1200 524.2549 286.0714 245.5229 144, 1510 Page 4 of 8 104.9108
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