Question

Juma spent half of his July salary on school fees .1/8 on farming and 2/3 of the remainder on food calculate his July salary if he spent 3200 on food

Answer 1

Answer is 12800

Answer 2

Let's calculate Juma's July salary step-by-step:

1. **Let Juma's July salary be \( S \).**

2. **Half of his salary spent on school fees:**
\[
\frac{S}{2}
\]

3. **Remaining salary after school fees:**
\[
S - \frac{S}{2} = \frac{S}{2}
\]

4. **One-eighth of his salary spent on farming:**
\[
\frac{1}{8} S
\]

5. **Remaining salary after farming:**
\[
\frac{S}{2} - \frac{1}{8} S = \frac{4S}{8} - \frac{S}{8} = \frac{3S}{8}
\]

6. **Two-thirds of the remainder spent on food:**
\[
\frac{2}{3} \left( \frac{3S}{8} \right) = \frac{2 \times 3S}{3 \times 8} = \frac{6S}{24} = \frac{S}{4}
\]

7. **Amount spent on food is given as 3200:**
\[
\frac{S}{4} = 3200
\]

8. **Solve for \( S \):**
\[
S = 3200 \times 4 = 12800
\]

So, Juma's July salary is \( 12,800 \) shillings.

Answer 3

Let's denote Juma's July salary as \( S \).

1. Juma spent half of his salary on school fees:
\[
\text{School fees} = \frac{1}{2} S
\]

2. After paying for school fees, the remainder of his salary is:
\[
\text{Remainder after school fees} = S - \frac{1}{2} S = \frac{1}{2} S
\]

3. Juma spent \( \frac{1}{8} \) of the remainder on farming:
\[
\text{Farming} = \frac{1}{8} \times \frac{1}{2} S = \frac{1}{16} S
\]

4. The remainder after school fees and farming is:
\[
\text{Remainder after school fees and farming} = \frac{1}{2} S - \frac{1}{16} S
\]

To simplify this, convert \( \frac{1}{2} S \) to sixteenths:
\[
\frac{1}{2} S = \frac{8}{16} S
\]
Now subtract the farming expenses:
\[
\text{Remainder} = \frac{8}{16} S - \frac{1}{16} S = \frac{7}{16} S
\]

5. Juma spent \( \frac{2}{3} \) of the remainder on food:
\[
\text{Food} = \frac{2}{3} \times \frac{7}{16} S = \frac{14}{48} S = \frac{7}{24} S
\]

6. It is given that Juma spent 3200 on food, so we have:
\[
\frac{7}{24} S = 3200
\]

7. To find \( S \), multiply both sides by the reciprocal of \( \frac{7}{24} \):
\[
S = 3200 \times \frac{24}{7}
\]

First, calculate \( 3200 \times 24 \):
\[
3200 \times 24 = 76800
\]

Now divide by 7:
\[
S = \frac{76800}{7} \approx 10971.43
\]

So, Juma's July salary is approximately \( 10971.43 \).

To round, Juma's July salary is approximately **10,971** when considering typical currency amounts.

Answer 4

Let’s re-evaluate the problem step by step to find Juma's salary correctly and verify where the error may have occurred.

1. **Let Juma's salary be \( S \)**.

2. **He spent half of his salary on school fees**:
\[
\text{School fees} = \frac{1}{2} S
\]

3. **Remaining salary after school fees**:
\[
\text{Remaining} = S - \frac{1}{2} S = \frac{1}{2} S
\]

4. **He spent \( \frac{1}{8} \) of the remaining salary on farming**:
\[
\text{Farming} = \frac{1}{8} \times \frac{1}{2} S = \frac{1}{16} S
\]

5. **Remaining salary after farming**:
\[
\text{Remaining after farming} = \frac{1}{2} S - \frac{1}{16} S
\]
To combine the fractions, convert \( \frac{1}{2} S \) to sixteenths:
\[
\frac{1}{2} S = \frac{8}{16} S
\]
Now, we can find the remainder:
\[
\text{Remaining} = \frac{8}{16} S - \frac{1}{16} S = \frac{7}{16} S
\]

6. **He spent \( \frac{2}{3} \) of the remaining salary on food**:
\[
\text{Food} = \frac{2}{3} \times \frac{7}{16} S = \frac{14}{48} S = \frac{7}{24} S
\]

7. **We know that he spent 3200 on food**:
\[
\frac{7}{24} S = 3200
\]

8. **To find \( S \)**, multiply both sides by the reciprocal of \( \frac{7}{24} \):
\[
S = 3200 \times \frac{24}{7}
\]

First, calculate \( 3200 \times 24 \):
\[
3200 \times 24 = 76800
\]

Now divide by 7:
\[
S = \frac{76800}{7} \approx 10971.43
\]

To solve for **exact integer values**, let's break it down again:

### Detailed Calculation
1. **Setup**:
\[
\frac{7}{24} S = 3200
\]

2. **Re-arranging**:
\[
S = 3200 \times \frac{24}{7}
\]

3. **Calculating**:
\[
3200 \times 24 = 76800 \quad \text{then,} \quad \frac{76800}{7} = 10971.43
\]

It seems that I have calculated it correctly based on the given ratios. However, if the answer is indeed **12800**, let's remap:

### Trying Another Approach to Confirm:
Assuming \( S \) may have been misrepresented or misunderstood, I’ll explore the direct information:
- Juma spent \( 3200 \) on food, which is \( \frac{7}{24} S \), we recalculate:

#### From Given Amount on Food
1. Start with:
\[
\frac{7}{24} S = 3200 \implies S = 3200 \times \frac{24}{7}
\]

2. This suggests:
\[
3200 \times 24 = 76800 \implies S = \frac{76800}{7} \approx 10971.43
\]

**Conclusion**:
The calculations yield approximately \( 10971 \), which conflicts with \( 12800 \). Please reconsider the starting assumptions, or verify details such as {\( S \), school fees, or food percentages}. This clarity may refine towards \( 12800 \). If there are changes or further details in spending breakdowns, these should be noted for accuracy.

Answer 5

Thank you for clarifying the steps! Let’s go through the calculations to confirm that Juma’s July salary is indeed \( 12,800 \) shillings.

1. **Let Juma's July salary be \( S \)**.

2. **Half of his salary spent on school fees**:
\[
\text{School fees} = \frac{S}{2}
\]

3. **Remaining salary after school fees**:
\[
\text{Remaining} = S - \frac{S}{2} = \frac{S}{2}
\]

4. **One-eighth of his salary spent on farming**:
\[
\text{Farming} = \frac{1}{8} S
\]

5. **Remaining salary after farming**:
\[
\text{Remaining after farming} = \frac{S}{2} - \frac{1}{8} S = \frac{4S}{8} - \frac{1}{8} S = \frac{3S}{8}
\]

6. **Two-thirds of the remainder spent on food**:
\[
\text{Food} = \frac{2}{3} \left( \frac{3S}{8} \right) = \frac{2 \times 3S}{3 \times 8} = \frac{6S}{24} = \frac{S}{4}
\]

7. **Amount spent on food is given as 3200**:
\[
\frac{S}{4} = 3200
\]

8. **Solve for \( S \)**:
\[
S = 3200 \times 4 = 12800
\]

Thus, Juma's July salary is indeed \( 12,800 \) shillings. Thank you for pointing out the correct breakdown of the expenses!