Let's determine the correct equation for the given problem. Here are the details:
Katie’s commute on the train takes 10 minutes more than [tex]\(\frac{1}{2}\)[/tex] the time it takes Mina to get to work.
Let [tex]\(x\)[/tex] represent the number of minutes it takes Mina to get to work.
According to the problem's description, Katie’s commute time is given by:
[tex]\[ \frac{1}{2} x + 10 \, \text{minutes} \][/tex]
We are also told that Katie’s commute time is 30 minutes. Thus, we can set up the following equation based on the given information:
[tex]\[ 30 = \frac{1}{2} x + 10 \][/tex]
Now, let's carefully consider the multiple-choice options:
1. [tex]\(30 = \frac{1}{2} x + 10\)[/tex] is our constructed equation.
2. [tex]\(30 = \frac{1}{2} x - 10\)[/tex] is incorrect because it subtracts 10 instead of adding.
3. [tex]\(30 = 2 x - 10\)[/tex] is incorrect because it multiplies [tex]\(x\)[/tex] by 2 and subtracts 10, instead of halving [tex]\(x\)[/tex] and adding 10.
4. [tex]\(30 = 2 x + 10\)[/tex] is incorrect because it multiplies [tex]\(x\)[/tex] by 2 and adds 10, differing from our problem’s setup.
Therefore, the correct equation is:
[tex]\[ 30 = \frac{1}{2} x + 10 \][/tex]
