EXPLANATION :
From the problem, the taxi charges a flat rate of $3 and an additional $0.50 per mile.
Let x = number of mile
and y = total cost
The equation will be :
[tex]y=3+0.50x[/tex]
Carl will take a taxi if the total cost is under $10.
Carl is 15 miles from home.
The inequality will be :
[tex]\begin{gathered} y\le10 \\ 3+0.50x\le10 \end{gathered}[/tex]
For him to take a taxi, otherwise he will take a bus.
Substitute x = 15 miles :
[tex]\begin{gathered} 3+0.50(15)\le10 \\ 3+7.50\le10 \\ 10.50\le10 \\ False \end{gathered}[/tex]
Since the total cost is greater than $10. He will take a bus.
ANSWER :
Carl will take a bus.
