Let R be the real area of the land. The title shows 13.5 hectares, which is 10% less than the real area.

Mathematics

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Answers

4 parts
a

15 hectares\text{15 hectares}

b

27\text{27}

c

23\frac{2}{3}

10 hectares\text{10 hectares}

d

shs 50,000,000\text{shs } 50,000,000

Step-by-step solution

12 steps

Here's the solution for Item 1:

Part a· 2 steps

Real area of the land.

  1. Let RR 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:

    13.5=R−0.10R13.5 = R - 0.10R 13.5=0.90R13.5 = 0.90R
  2. Solve for RR.

    R=13.50.90R = \frac{13.5}{0.90} R=15 hectaresR = 15 \text{ hectares}

    The real area of the land is 15 hectares\boxed{\text{15 hectares}}.

Part b

27\text{27}

2-digit PIN for the suitcase

  1. Let the two-digit PIN be 10x+y10x + y, where xx is the first digit and yy is the second digit.

    From the problem statement, we have two conditions:

    1. The PIN is three times the sum of its digits: 10x+y=3(x+y)(1)10x + y = 3(x + y) \quad (1)
    2. The second digit is five more than the first digit: y=x+5(2)y = x + 5 \quad (2)
  2. Substitute equation (2) into equation (1).

    10x+(x+5)=3(x+(x+5))10x + (x + 5) = 3(x + (x + 5)) 11x+5=3(2x+5)11x + 5 = 3(2x + 5) 11x+5=6x+1511x + 5 = 6x + 15
  3. Solve for xx.

    11x−6x=15−511x - 6x = 15 - 5 5x=105x = 10 x=2x = 2
  4. Substitute the value of xx back into equation (2) to find yy.

    y=2+5y = 2 + 5 y=7y = 7
  5. Form the PIN using the values of xx and yy.

    The PIN is 10(2)+7=20+7=2710(2) + 7 = 20 + 7 = 27.
    The 2-digit PIN for the suitcase is 27\boxed{\text{27}}.

Part c

23\frac{2}{3}

Simplified fraction of the whole land used for agriculture and hence determine the real area of the land for agriculture.

  1. Convert the repeating decimal 0.666... to a simplified fraction.

    Let f=0.666...f = 0.666...
    Multiply by 10: 10f=6.666...10f = 6.666...
    Subtract the first equation from the second:

    10f−f=6.666...−0.666...10f - f = 6.666... - 0.666... 9f=69f = 6 f=69=23f = \frac{6}{9} = \frac{2}{3}

    The simplified fraction of the whole land used for agriculture is 23\boxed{\frac{2}{3}}.

  2. 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) ×\times (real area of land)

    Area for agriculture=23×15 hectares\text{Area for agriculture} = \frac{2}{3} \times 15 \text{ hectares} Area for agriculture=10 hectares\text{Area for agriculture} = 10 \text{ hectares}

    The real area of the land for agriculture is 10 hectares\boxed{\text{10 hectares}}.

Part d

shs 50,000,000\text{shs } 50,000,000

Amount of money to get from the sell of land.

  1. 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).

    Remaining land=15 hectares−10 hectares=5 hectares\text{Remaining land} = 15 \text{ hectares} - 10 \text{ hectares} = 5 \text{ hectares}
  2. Calculate the area of land sold.

    The problem states 15\frac{1}{5} of the remaining land is sold.

    Area sold=15×5 hectares=1 hectare\text{Area sold} = \frac{1}{5} \times 5 \text{ hectares} = 1 \text{ hectare}
  3. Calculate the amount of money obtained from the sale.

    The selling price is shs 50 millions per hectare.

    Amount of money=1 hectare×shs 50,000,000/hectare\text{Amount of money} = 1 \text{ hectare} \times \text{shs } 50,000,000/\text{hectare} Amount of money=shs 50,000,000\text{Amount of money} = \text{shs } 50,000,000

    The amount of money to get from the sell of land is shs 50,000,000\boxed{\text{shs } 50,000,000}.

    2 zimekamilika. Zimebaki 3 leo — tuma inayofuata.

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