Question

A family used two fifth of it's monthly income on school fees . Three quarters of the remaining was used on family upkeep while the rest was invested. The family invested ksh 13500monthly . Calculate the amount of money the family used on school fees every month

Answer 1

Let the family's monthly income be represented as \( I \).

1. The family used two-fifths of its monthly income on school fees:
\[
\text{School Fees} = \frac{2}{5} I
\]

2. The amount remaining after school fees is:
\[
\text{Remaining Income} = I - \frac{2}{5} I = \frac{3}{5} I
\]

3. The family used three-quarters of the remaining income for upkeep:
\[
\text{Family Upkeep} = \frac{3}{4} \left( \frac{3}{5} I \right) = \frac{9}{20} I
\]

4. The rest of the income was invested. The remaining income after school fees and upkeep is:
\[
\text{Remaining After Upkeep} = \frac{3}{5} I - \frac{9}{20} I
\]

To subtract these fractions, we need a common denominator. The least common multiple of 5 and 20 is 20.

Convert \(\frac{3}{5} I\) to have a denominator of 20:
\[
\frac{3}{5} I = \frac{12}{20} I
\]

Now subtract:
\[
\text{Remaining After Upkeep} = \frac{12}{20} I - \frac{9}{20} I = \frac{3}{20} I
\]

5. We know that this remaining amount is invested, and the family invested ksh 13,500:
\[
\frac{3}{20} I = 13500
\]

6. Now, solve for \( I \):
\[
I = 13500 \times \frac{20}{3} = 13500 \times \frac{20}{3} = 90000
\]

7. Now we can find the amount of money used on school fees:
\[
\text{School Fees} = \frac{2}{5} I = \frac{2}{5} \times 90000 = \frac{180000}{5} = 36000
\]

Thus, the amount of money the family used on school fees every month is **ksh 36,000**.