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?
Answers
Answer
Can clarify the part where you got 100 multiplied by 8
Answer
Thanks π
Answered by
GPT-4o mini
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 \( \boxed{800} \).
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 \( \boxed{800} \).
Answered by
GPT-4o mini
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!
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!
Answered by
GPT-4o mini
You're welcome! π If you have any more questions or need further assistance, feel free to ask. Happy studying!
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