Question

Two friends go shares in a car. Brian pays 1/4 and Don pays 3/8 of the total price of the car. The balance of K300 is loaned to them by Don's mother. How much does the car cost?

Answer 1

Let the total cost of the car be \( x \).

According to the problem:
- Brian pays \( \frac{1}{4}x \)
- Don pays \( \frac{3}{8}x \)

The sum of their contributions and the loan from Don's mother should equal the total cost of the car:

\[
\frac{1}{4}x + \frac{3}{8}x + 300 = x
\]

To combine the fractions, we first need a common denominator. The least common multiple of 4 and 8 is 8. We can rewrite \( \frac{1}{4}x \) in terms of eighths:

\[
\frac{1}{4}x = \frac{2}{8}x
\]

Now substituting back into the equation, we get:

\[
\frac{2}{8}x + \frac{3}{8}x + 300 = x
\]

Combining the fractions on the left side:

\[
\frac{2 + 3}{8}x + 300 = x
\]

This simplifies to:

\[
\frac{5}{8}x + 300 = x
\]

To isolate \( x \), we subtract \( \frac{5}{8}x \) from both sides:

\[
300 = x - \frac{5}{8}x
\]

This simplifies to:

\[
300 = \frac{3}{8}x
\]

Now, to find \( x \), we multiply both sides by \( \frac{8}{3} \):

\[
x = 300 \cdot \frac{8}{3}
\]

Calculating this gives:

\[
x = 300 \cdot \frac{8}{3} = 100 \cdot 8 = 800
\]

Thus, the total cost of the car is \( \boxed{800} \).

Answer 2

Can clarify the part where you got 100 multiplied by 8

Answer 3

Sure! Let's walk through that step more carefully.

We arrived at the equation:

\[
x = 300 \cdot \frac{8}{3}
\]

This means we need to multiply 300 by \( \frac{8}{3} \).

To do this calculation:

1. **Divide 300 by 3**:
\[
300 \div 3 = 100
\]

2. **Now multiply the result by 8**:
\[
100 \cdot 8 = 800
\]

Thus, we found that:

\[
x = 800
\]

So, the total cost of the car is indeed \( \boxed{800} \).

Let me know if you have any more questions!

Answer 4

Thanks 😊

Answer 5

You're welcome! 😊 If you have any more questions or need further assistance, feel free to ask. Happy studying!