Question

The fare for a taxi cab is $2.50 per passenger and $0.75 for each mile. A group of friends has $22.00

A. Write a linear inequality to represent how many miles,Y, the group can travel if there are x people in the group.

B. If there are 3 people in the group, how far can they travel by taxi?

C. If the group wants fo travel 10 miles, what is the greatest number if passengers that can travel by taxi? Explain.

Answer 1

For this case we have to:

x: Let the variable representing the number of people to travel in the group

y: Let the variable representing the number of miles traveled.

If friends only have $22 then we have the following inequality:

`2.50x + 0.75y \leq22`

Now, if there are three people in the group we have that
`x = 3.`

`2.50 (3) + 0.75y \leq22\\7.5 + 0.75y \leq22\\0.75y \leq22-7.5\\0.75y \leq14.5\\y\leq \frac {14.5} {0.75}\\y\leq19.33`

The taxi can travel a maximum of 19.33 miles.

On the other hand, if the group wants to travel 10 miles then we have to y = 10.

`2.50x + 0.75 (10) \leq22\\2.50x + 7.5 \leq22\\2.50x \leq22-7.5\\2.50x \leq14.5\\x\leq \frac {14.5} {2.50}\\x \leq5.8`

Thus, they could travel a maximum of 5 people.

ANswer:

`2.50x + 0.75y \leq22`

Traveling 3 people, the taxi can travel a maximum of 19.33 miles

Traveling 10 miles, a maximum of 5 people can travel