Hiroshi spends 30 minutes on history homework and 60 minutes on English homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?
[tex]$\frac{1}{4}(x+30+60)=x$[/tex]
[tex]$\frac{1}{4}(x)=x(30+60)$[/tex]
[tex]$\frac{1}{4} x(30+60)=x$[/tex]
[tex]$\frac{1}{4}(x)=(30+60)$[/tex]
Answer (1)
Define x as the time spent on math homework.
Express the total homework time as 30 + 60 + x .
Set up the equation 4 1 ( 30 + 60 + x ) = x .
Solve for x to find the time spent on math: 30 .
Explanation
Problem Analysis and Setup Let's analyze the problem. We know Hiroshi spends 30 minutes on history and 60 minutes on English homework. We also know that one-fourth of his total homework time is spent on math. Our goal is to find out how much time he spends on math homework. Let's denote the time spent on math homework as x . The total homework time is the sum of the time spent on history, English, and math, which is 30 + 60 + x . Since one-fourth of the total homework time is spent on math, we can write the equation 4 1 ( 30 + 60 + x ) = x . Now, we need to solve this equation for x .
Solving the Equation Now, let's solve the equation 4 1 ( 30 + 60 + x ) = x . First, simplify the equation: 4 1 ( 90 + x ) = x
Multiply both sides by 4 to get rid of the fraction: 90 + x = 4 x
Subtract x from both sides: 90 = 3 x
Divide both sides by 3: x = 3 90 x = 30
Verification So, Hiroshi spends 30 minutes on his math homework. Let's check our answer. Total homework time is 30 + 60 + 30 = 120 minutes. One-fourth of the total time is 4 1 × 120 = 30 minutes, which is the time he spends on math. Our answer is correct.
Final Answer Therefore, Hiroshi spends 30 minutes on his math homework.
Examples
Understanding how to manage time effectively is a crucial skill. Suppose you have a total of 2 hours (120 minutes) for homework and you want to allocate one-fourth of your time to math. This problem demonstrates how to calculate exactly how many minutes you should dedicate to math so that you can plan your study schedule accordingly. By setting up and solving a simple equation, you can ensure you're distributing your time wisely across different subjects, leading to better academic performance and reduced stress.
