To determine the total cost for a car service that travels 30 miles, we can use the given equation for the total cost [tex]\( y \)[/tex], where [tex]\( y = 0.5x + 5 \)[/tex] and [tex]\( x \)[/tex] represents the number of miles.
Given [tex]\( x = 30 \)[/tex] miles, we can substitute [tex]\( x \)[/tex] into the equation and solve for [tex]\( y \)[/tex] as follows:
1. Substitute [tex]\( 30 \)[/tex] for [tex]\( x \)[/tex] in the equation [tex]\( y = 0.5x + 5 \)[/tex]:
[tex]\[
y = 0.5 \times 30 + 5
\][/tex]
2. First, calculate [tex]\( 0.5 \times 30 \)[/tex]:
[tex]\[
0.5 \times 30 = 15
\][/tex]
3. Next, add the flat rate of $5 to the result:
[tex]\[
y = 15 + 5
\][/tex]
4. Adding these values together gives us:
[tex]\[
y = 20
\][/tex]
Therefore, the total cost for traveling 30 miles is [tex]\( \boxed{20} \)[/tex] dollars.
