To solve the first part of the problem involving the parcel of land shared by the three brothers (Kirk, Mojo, and Kramer), we can follow these steps:
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Determine the total parcel of land:
- We know that Kramer received the remaining portion of the land, which is 24 acres.
- The shares are distributed as follows:
- Kirk: \( \frac{1}{3} \)
- Mojo: \( \frac{2}{5} \)
- Kramer: Remaining (let's call it \( x \))
Since the total shares must equal 1 (or 100%), we can express this mathematically as:
\[ \frac{1}{3} + \frac{2}{5} + x = 1 \]
We need to determine \( x \). To combine these fractions, we first find a common denominator, which is 15.
\[ \frac{1}{3} = \frac{5}{15}, \quad \frac{2}{5} = \frac{6}{15} \]
Now substitute:
\[ \frac{5}{15} + \frac{6}{15} + x = 1 \] \[ \frac{11}{15} + x = 1 \]
To solve for \( x \):
\[ x = 1 - \frac{11}{15} = \frac{4}{15} \]
This means Kramer owns \( \frac{4}{15} \) of the total land, which corresponds to the 24 acres he has. Now we can find the total land area.
If \( \frac{4}{15} \) of the total land \( L \) is 24 acres, we set up the equation:
\[ \frac{4}{15}L = 24 \]
To find \( L \), multiply both sides by \( \frac{15}{4} \):
\[ L = 24 \times \frac{15}{4} = 90 \text{ acres} \]
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Find the land sizes for Kirk and Mojo:
Now that we know the total land is 90 acres, we can find how much land each brother has:
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Kirk: \[ \frac{1}{3} \times 90 = 30 \text{ acres} \]
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Mojo: \[ \frac{2}{5} \times 90 = 36 \text{ acres} \]
To find the parcel of land shared between Kirk and Mojo:
\[ \text{Parcel shared} = Kirk + Mojo = 30 + 36 = 66 \text{ acres} \]
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Size of land Mojo has more than Kirk:
\[ \text{Mojo's land} - \text{Kirk's land} = 36 - 30 = 6 \text{ acres} \]
Summary of the answers for part 1:
- The parcel of land shared between Kirk and Mojo is 66 acres.
- Mojo has 6 acres more than Kirk.
Part B: Calculation of interest
To find out how many years it would take for Ghana cedis 8,000.00 to yield an interest of Ghana cedis 2,000.00 at a simple interest rate of 10%, we can use the formula for simple interest:
\[ I = P \times r \times t \]
Where:
- \( I \) is the interest earned (2000 GHS)
- \( P \) is the principal amount (8000 GHS)
- \( r \) is the rate of interest (10% or 0.10)
- \( t \) is the time in years
Substituting the values we have:
\[ 2000 = 8000 \times 0.10 \times t \]
This simplifies to:
\[ 2000 = 800 \times t \]
Now we can solve for \( t \):
\[ t = \frac{2000}{800} = 2.5 \text{ years} \]
Summary of the answer for part B:
It would take 2.5 years for Ghana cedis 8,000.00 to yield an interest of Ghana cedis 2,000.00 at a simple interest rate of 10%.