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QuestionGrade 12 Math: Analyze the 2023 North West budget table. Answer questions on budget meaning, highest allocation, and find XX, YY, ZZ.

Studdy Solution

STEP 1

Assumptions1. The budget allocations are given in thousands of Rands. . The range of allocation for the2023/24 financial year is R20,093,300.
3. The total allocation for the2023/24 financial year is denoted by Y.
4. The allocation for the Office of the Premier in the2023/24 financial year is denoted by X.
5. The allocation for Social Development in the2024/25 financial year is denoted by Z.
6. The mean allocation for the2024/25 financial year is R3,994,769.

STEP 2

To answer1.1.2, we need to identify the department that received the highest allocation in the202/24 financial year. We can do this by comparing the allocations of all departments.

STEP 3

From the table, it is clear that the department with the highest allocation in the2023/24 financial year is the Education department with an allocation of20575,5 thousand Rands.

STEP 4

To answer1.1.3, we need to identify the department(s) that will receive less allocation in the2024/25 financial year compared to the2023/24 financial year. We can do this by comparing the allocations of each department in both years.

STEP 5

From the table, it is clear that the departments that will receive less allocation in the2024/25 financial year compared to the2023/24 financial year are the Office of the Premier, Economic Development, Environment, Conservation and Tourism, Cooperative Governance and Traditional Affairs, and Public Works and Roads.

STEP 6

To answer1.1.4, we need to determine the minimum value of X. Given that the range of allocation for the2023/24 financial year is R20,093,300, we can calculate X by subtracting the highest allocation from the range.
X=Range−Highest allocationX = Range - Highest\, allocation

STEP 7

Plug in the values for the range and the highest allocation to calculate X.
X=20093,3−20575,5X =20093,3 -20575,5

STEP 8

Calculate the value of X.
X=20093,3−20575,5=−482,2X =20093,3 -20575,5 = -482,2Since the allocation cannot be negative, the minimum value of X should be0.

STEP 9

To answer..5, we need to calculate the missing value Y, the total allocation for the2023/24 financial year. We can do this by adding up all the allocations of the departments.
Y=∑i=nAllocationiY = \sum_{i=}^{n} Allocation_i

STEP 10

Plug in the values for the allocations to calculate Y.
Y=X+503,4+15219,6+742,+2332,9+1009,3+565,9+20575,5+659,3+3824,5+1713,+1229,4+1999,2Y = X +503,4 +15219,6 +742, +2332,9 +1009,3 +565,9 +20575,5 +659,3 +3824,5 +1713, +1229,4 +1999,2

STEP 11

Since we have determined that the minimum value of X should be0, we can replace X with0 in the equation.
Y=0+503,4+15219,6+742,+233,9+1009,3+565,9+20575,5+659,3+3824,5+1713,+1229,4+1999,Y =0 +503,4 +15219,6 +742, +233,9 +1009,3 +565,9 +20575,5 +659,3 +3824,5 +1713, +1229,4 +1999,

STEP 12

Calculate the value of Y.
Y=0+503,4+15219,6+742,+2332,9+1009,+565,9+20575,5+659,+3824,5+171,+1229,4+1999,2=45284,7Y =0 +503,4 +15219,6 +742, +2332,9 +1009, +565,9 +20575,5 +659, +3824,5 +171, +1229,4 +1999,2 =45284,7The total allocation for the202/24 financial year is45284,7 thousand Rands.

STEP 13

To answer..6, we need to calculate the missing value Z, the allocation for Social Development. Given that the mean allocation for the202/25 financial year is R3,994,769, we can calculate Z by multiplying the mean allocation by the number of departments and then subtracting the sum of the known allocations.
Z=Mean allocation×Number of departments−∑i=nKnown allocationsZ = Mean\, allocation \times Number\, of\, departments - \sum_{i=}^{n} Known\, allocations

STEP 14

Plug in the values for the mean allocation, the number of departments, and the known allocations to calculate Z.
Z=3994,769×13−(496,7+511,3+15841,+768,0+2408,4+1008,2+585,6+21053,8+652,+3489,8+1267,3+208,0)Z =3994,769 \times13 - (496,7 +511,3 +15841, +768,0 +2408,4 +1008,2 +585,6 +21053,8 +652, +3489,8 +1267,3 +208,0)

STEP 15

Calculate the value of Z.
Z=3994,769×13−(496,7+511,3+15841,+768,0+2408,4+1008,2+585,+21053,8+652,+3489,8+1267,3+2085,0)=51938,997−33168,3Z =3994,769 \times13 - (496,7 +511,3 +15841, +768,0 +2408,4 +1008,2 +585, +21053,8 +652, +3489,8 +1267,3 +2085,0) =51938,997 -33168,3Z=18770,697Z =18770,697The allocation for Social Development in the2024/25 financial year is18770,697 thousand Rands.

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