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A) Gross profits will she earn from her heaps after re-packaging?

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2 parts
a

Ugx 4500\text{Ugx } 4500

b

Ugx 30000\text{Ugx } 30000

Step-by-step solution

11 steps

Here are the solutions to your questions:

Part a· 6 steps

Gross profits will she earn from her heaps after re-packaging?

  1. Calculate the total number of tomatoes bought.

    She bought 9 heaps, with 8 tomatoes per heap.

    Total tomatoes=9 heaps×8 tomatoes/heap=72 tomatoes\text{Total tomatoes} = 9 \text{ heaps} \times 8 \text{ tomatoes/heap} = 72 \text{ tomatoes}

  2. Calculate the total cost of buying the tomatoes before the discount.

    The cost was Ugx 2000 per heap.

    Cost before discount=9 heaps×Ugx 2000/heap=Ugx 18000\text{Cost before discount} = 9 \text{ heaps} \times \text{Ugx } 2000/\text{heap} = \text{Ugx } 18000

  3. Calculate the total cost after the 5% discount.

    Discount amount=0.05×Ugx 18000=Ugx 900\text{Discount amount} = 0.05 \times \text{Ugx } 18000 = \text{Ugx } 900 Total cost after discount=Ugx 18000−Ugx 900=Ugx 17100\text{Total cost after discount} = \text{Ugx } 18000 - \text{Ugx } 900 = \text{Ugx } 17100

  4. Calculate the number of new heaps after re-packaging.

    She re-packages into heaps of four tomatoes.

    Number of new heaps=72 tomatoes4 tomatoes/heap=18 heaps\text{Number of new heaps} = \frac{72 \text{ tomatoes}}{4 \text{ tomatoes/heap}} = 18 \text{ heaps}

  5. Calculate the total revenue from selling the new heaps.

    She sells each new heap for Ugx 1200.

    Total revenue=18 heaps×Ugx 1200/heap=Ugx 21600\text{Total revenue} = 18 \text{ heaps} \times \text{Ugx } 1200/\text{heap} = \text{Ugx } 21600

  6. Calculate the gross profit.

    Gross profit is total revenue minus total cost.

    Gross profit=Ugx 21600−Ugx 17100=Ugx 4500\text{Gross profit} = \text{Ugx } 21600 - \text{Ugx } 17100 = \boxed{\text{Ugx } 4500}

Part b

Ugx 30000\text{Ugx } 30000

Money, will she spend in total to buy the tickets she needs?

  1. Define variables for ticket prices.

    Let AA be the cost of an adult ticket and CC be the cost of a child ticket.

  2. Formulate equations based on the given information.

    From the uncle's visit (1 adult, 3 children) in Dec 2023:

    A+3C=17000(1)A + 3C = 17000 \quad (1)

    From Mr. and Mrs. Mukasa's visit (2 adults, 1 child) in June 2024:

    2A+C=14000(2)2A + C = 14000 \quad (2)

  3. Solve the system of equations for AA and CC.

    From equation (2), express CC in terms of AA:

    C=14000−2AC = 14000 - 2A

    Substitute this into equation (1):

    A+3(14000−2A)=17000A + 3(14000 - 2A) = 17000 A+42000−6A=17000A + 42000 - 6A = 17000 −5A=17000−42000-5A = 17000 - 42000 −5A=−25000-5A = -25000 A=−25000−5=5000A = \frac{-25000}{-5} = 5000

    Now substitute A=5000A = 5000 back into the expression for CC:

    C=14000−2(5000)=14000−10000=4000C = 14000 - 2(5000) = 14000 - 10000 = 4000

    So, an adult ticket costs Ugx 5000 and a child ticket costs Ugx 4000.

  4. Determine the number of adults and children in her group.

    She plans to buy tickets for herself, her husband, and five children.

    Number of adults=1(herself)+1(husband)=2\text{Number of adults} = 1 (\text{herself}) + 1 (\text{husband}) = 2 Number of children=5\text{Number of children} = 5

  5. Calculate the total cost for her group.

    The park charges are adjusted every five years, and all visits (Dec 2023, June 2024, Dec 2024) fall within the same 5-year period, so the prices remain consistent.

    Total cost=(2×A)+(5×C)\text{Total cost} = (2 \times A) + (5 \times C) Total cost=(2×Ugx 5000)+(5×Ugx 4000)\text{Total cost} = (2 \times \text{Ugx } 5000) + (5 \times \text{Ugx } 4000) Total cost=Ugx 10000+Ugx 20000\text{Total cost} = \text{Ugx } 10000 + \text{Ugx } 20000 Total cost=Ugx 30000\text{Total cost} = \boxed{\text{Ugx } 30000}
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