To determine which equation correctly represents the problem, let's break it down step-by-step.
Grace and her dad are attending the state fair where the cost of an adult ticket is [tex]$15.
We need to find how much Grace will pay for a student ticket, with the price of an adult ticket being given as \(\$[/tex]15\) and it's mentioned that this is half the price of a student ticket plus 8.
Let [tex]\( x \)[/tex] represent the price of a student ticket. According to the problem, half the price of a student ticket plus 8 equals the price of an adult ticket ($15). So we can set up the equation as follows:
1. Start by defining the relationship given:
[tex]\[
\frac{1}{2}x + 8 = 15
\][/tex]
This matches the given conditions. Now let’s check this against the possible options provided:
- [tex]\(\frac{1}{2} x + 8 = 15\)[/tex]
- [tex]\(\frac{1}{2} x - 8 = 15\)[/tex]
- [tex]\(\frac{1}{2} x + 15 = 8\)[/tex]
- [tex]\(\frac{1}{2} x - 15 = 8\)[/tex]
The correct equation among these options is:
[tex]\[
\frac{1}{2} x + 8 = 15
\][/tex]
So, the correct option is:
[tex]\[
\boxed{\frac{1}{2} x + 8 = 15}
\][/tex]
