Explore a wide range of topics and get answers from experts on IDNLearn.com. Our platform is designed to provide quick and accurate answers to any questions you may have.
Sagot :
Let's solve this step-by-step by understanding the problem and analyzing each option given:
1. Understanding the problem:
- Hiroshi spends 30 minutes on history homework.
- Hiroshi spends 60 minutes on English homework.
- Hiroshi spends [tex]\( x \)[/tex] minutes on math homework.
- One fourth of Hiroshi's total homework time is spent on math homework.
2. Writing the total homework time:
- The total homework time [tex]\( T \)[/tex] consists of the sum of history, English, and math homework times.
- [tex]\( T = 30 + 60 + x \)[/tex]
- Simplify this to:
[tex]\[ T = 90 + x \][/tex]
3. Expressing the given condition in mathematical terms:
- One fourth of the total homework time [tex]\( T \)[/tex] is spent on math homework.
- The math homework time is [tex]\( x \)[/tex].
- Therefore, we can write:
[tex]\[ \frac{1}{4} \cdot (90 + x) = x \][/tex]
Now let's compare this derived equation with the given options:
### Option 1: [tex]\(\frac{1}{4}(x + 30 + 60) = x\)[/tex]
- Simplify the equation inside the parenthesis:
[tex]\[ \frac{1}{4}(x + 30 + 60) = \frac{1}{4}(x + 90) \][/tex]
- This simplifies to:
[tex]\[ \frac{1}{4} \cdot (90 + x) = x \][/tex]
- This matches our derived equation.
### Option 2: [tex]\(\frac{1}{4}(x) = x(30 + 60)\)[/tex]
- Simplify the equation:
[tex]\[ \frac{1}{4} \cdot x = x \cdot 90 \][/tex]
- This means:
[tex]\[ \frac{x}{4} = 90x \][/tex]
- This equation does not make sense considering the problem statement. It implies that [tex]\( x \)[/tex] should be both large and small simultaneously.
### Option 3: [tex]\(\frac{1}{4} x(30 + 60) = x\)[/tex]
- Simplify the equation inside the parenthesis:
[tex]\[ \frac{1}{4} \cdot x \cdot 90 = x \][/tex]
- This means:
[tex]\[ \frac{90x}{4} = x \quad \text{or} \quad 22.5x = x \][/tex]
- This equation does not make logical sense.
### Option 4: [tex]\(\frac{1}{4}(x) = (30 + 60)\)[/tex]
- Simplify the equation inside the parenthesis:
[tex]\[ \frac{x}{4} = 90 \][/tex]
- This means:
[tex]\[ x = 360 \][/tex]
- This is a numerical solution but does not frame the correct time relationship described in the problem.
### Conclusion:
The only equation that matches our derived condition is:
[tex]\[\boxed{\frac{1}{4}(x + 30 + 60) = x}\][/tex]
1. Understanding the problem:
- Hiroshi spends 30 minutes on history homework.
- Hiroshi spends 60 minutes on English homework.
- Hiroshi spends [tex]\( x \)[/tex] minutes on math homework.
- One fourth of Hiroshi's total homework time is spent on math homework.
2. Writing the total homework time:
- The total homework time [tex]\( T \)[/tex] consists of the sum of history, English, and math homework times.
- [tex]\( T = 30 + 60 + x \)[/tex]
- Simplify this to:
[tex]\[ T = 90 + x \][/tex]
3. Expressing the given condition in mathematical terms:
- One fourth of the total homework time [tex]\( T \)[/tex] is spent on math homework.
- The math homework time is [tex]\( x \)[/tex].
- Therefore, we can write:
[tex]\[ \frac{1}{4} \cdot (90 + x) = x \][/tex]
Now let's compare this derived equation with the given options:
### Option 1: [tex]\(\frac{1}{4}(x + 30 + 60) = x\)[/tex]
- Simplify the equation inside the parenthesis:
[tex]\[ \frac{1}{4}(x + 30 + 60) = \frac{1}{4}(x + 90) \][/tex]
- This simplifies to:
[tex]\[ \frac{1}{4} \cdot (90 + x) = x \][/tex]
- This matches our derived equation.
### Option 2: [tex]\(\frac{1}{4}(x) = x(30 + 60)\)[/tex]
- Simplify the equation:
[tex]\[ \frac{1}{4} \cdot x = x \cdot 90 \][/tex]
- This means:
[tex]\[ \frac{x}{4} = 90x \][/tex]
- This equation does not make sense considering the problem statement. It implies that [tex]\( x \)[/tex] should be both large and small simultaneously.
### Option 3: [tex]\(\frac{1}{4} x(30 + 60) = x\)[/tex]
- Simplify the equation inside the parenthesis:
[tex]\[ \frac{1}{4} \cdot x \cdot 90 = x \][/tex]
- This means:
[tex]\[ \frac{90x}{4} = x \quad \text{or} \quad 22.5x = x \][/tex]
- This equation does not make logical sense.
### Option 4: [tex]\(\frac{1}{4}(x) = (30 + 60)\)[/tex]
- Simplify the equation inside the parenthesis:
[tex]\[ \frac{x}{4} = 90 \][/tex]
- This means:
[tex]\[ x = 360 \][/tex]
- This is a numerical solution but does not frame the correct time relationship described in the problem.
### Conclusion:
The only equation that matches our derived condition is:
[tex]\[\boxed{\frac{1}{4}(x + 30 + 60) = x}\][/tex]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Thank you for visiting IDNLearn.com. For reliable answers to all your questions, please visit us again soon.
