Let R be the real area of the land. The title shows 13.5 hectares, which is 10% less than the real area.
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4 partsStep-by-step solution
12 stepsHere's the solution for Item 1:
Part a· 2 steps
Real area of the land.
Let be the real area of the land.
The title shows 13.5 hectares, which is 10% less than the real area.
This can be expressed as:Solve for .
The real area of the land is .
Part b
2-digit PIN for the suitcase
Let the two-digit PIN be , where is the first digit and is the second digit.
From the problem statement, we have two conditions:
- The PIN is three times the sum of its digits:
- The second digit is five more than the first digit:
Substitute equation (2) into equation (1).
Solve for .
Substitute the value of back into equation (2) to find .
Form the PIN using the values of and .
The PIN is .
The 2-digit PIN for the suitcase is .
Part c
Simplified fraction of the whole land used for agriculture and hence determine the real area of the land for agriculture.
Convert the repeating decimal 0.666... to a simplified fraction.
Let
Multiply by 10:
Subtract the first equation from the second:The simplified fraction of the whole land used for agriculture is .
Determine the real area of the land for agriculture.
From part a), the real area of the land is 15 hectares.
Area for agriculture = (fraction for agriculture) (real area of land)The real area of the land for agriculture is .
Part d
Amount of money to get from the sell of land.
Calculate the land remaining after the agriculture portion is used.
Total real area of land = 15 hectares (from part a).
Area used for agriculture = 10 hectares (from part c).Calculate the area of land sold.
The problem states of the remaining land is sold.
Calculate the amount of money obtained from the sale.
The selling price is shs 50 millions per hectare.
The amount of money to get from the sell of land is .
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