Question

Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.65 per mile. Katie has no more than $10 to spend on a ride.(1) What ia your variable and what does it represent?(2) Write your inequality : (3) Solve your inequality :(4) Explain what your solution means for katie : (5) Does katie have enough money for a 10 mile ride? Please explain. (6) If the ride is 11.5 miles how much will katie be charged?

Answer 1

(1)

Let:

x = Number of miles traveled

(2)

`1.75+0.65x\le10`

(3)

`\begin{gathered} \text{subtract 1.75 from both sides:} \\ 1.75+0.65x-1.75\le10-1.75 \\ 0.65x\le8.25 \\ \text{divide both sides by 0.65:} \\ (0.65x)/(0.65)\le(8.25)/(0.65) \\ x\le12.69mi \end{gathered}`

(4)

This means Katie can travel a maximum of 12.69 miles

(5)

Yes, she does

`\begin{gathered} 1.75+0.65(10)\le10 \\ 8.25\le10 \end{gathered}`

(6)

`\begin{gathered} x=11.5 \\ 1.75+0.65(11.5)\le10 \\ 9.225\le10 \end{gathered}`

$9.225