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A group of 3 people spent GH¢600.00 for 10 days. How much will 5 people spend for 8 days?

Mathematics

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Answer

2

6 boys\text{6 boys}

GH¢ 800.00\text{GH¢ 800.00}

Step-by-step solution

4 steps

Here are the solutions to your homework questions:

Part 1· 2 steps

This is an inverse proportion problem. The total work (task) is constant.
Let BB be the number of boys and TT be the time in hours.
The product B×TB \times T remains constant.

  1. Calculate the total work units.

    B1×T1=36 boys×4 hours=144 boy-hoursB_1 \times T_1 = 36 \text{ boys} \times 4 \text{ hours} = 144 \text{ boy-hours}

  2. Use the total work units to find the new number of boys (B2B_2) for the new time (T2=24T_2 = 24 hours).

    B2×T2=144 boy-hoursB_2 \times T_2 = 144 \text{ boy-hours} B2×24 hours=144 boy-hoursB_2 \times 24 \text{ hours} = 144 \text{ boy-hours} B2=144 boy-hours24 hoursB_2 = \frac{144 \text{ boy-hours}}{24 \text{ hours}} B2=6 boysB_2 = 6 \text{ boys}

    The number of boys required is 6 boys.

Part 2

6 boys\text{6 boys}

This is a direct proportion problem. The cost is directly proportional to the number of people and the number of days.
Let PP be the number of people, DD be the number of days, and CC be the cost.
The ratio CP×D\frac{C}{P \times D} remains constant.

  1. Calculate the cost per person per day.

    Cost per person per day=C1P1×D1\text{Cost per person per day} = \frac{C_1}{P_1 \times D_1} Cost per person per day=GH¢ 600.003 people×10 days\text{Cost per person per day} = \frac{\text{GH¢ } 600.00}{3 \text{ people} \times 10 \text{ days}} Cost per person per day=GH¢ 600.0030 person-days\text{Cost per person per day} = \frac{\text{GH¢ } 600.00}{30 \text{ person-days}} Cost per person per day=GH¢ 20.00 per person-day\text{Cost per person per day} = \text{GH¢ } 20.00 \text{ per person-day}

  2. Calculate the total cost for 5 people staying for 8 days.

    C2=(Cost per person per day)×P2×D2C_2 = (\text{Cost per person per day}) \times P_2 \times D_2 C2=GH¢ 20.00/person-day×5 people×8 daysC_2 = \text{GH¢ } 20.00/\text{person-day} \times 5 \text{ people} \times 8 \text{ days} C2=GH¢ 20.00×40C_2 = \text{GH¢ } 20.00 \times 40 C2=GH¢ 800.00C_2 = \text{GH¢ } 800.00

    The cost for 5 people staying for 8 days is GH¢ 800.00.

    Here are your final answers:

    1. The number of boys required is 6 boys\boxed{\text{6 boys}}.
    2. The cost for 5 people staying for 8 days is GH¢ 800.00\boxed{\text{GH¢ 800.00}}.
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