Question

A cable car can safely carry n people. There are already 3/4 n people on the cable car. Only 12 more people can board the cable car before it becomes unsafe. How many people at most can the cable car carry? Write an inequality then solve.

Answer 1

Answer: At most 36 people can carry the cable car.

Explanation:

There are already 3/4 n people on the cable car.

Also, Only 12 more people can board the cable car before it becomes unsafe.

Hence, After coming 12 people, the total number of people in the cable car

=
`(3)/(4) n + 12`

According to the question,

A cable car can safely carry n people.

⇒
`(3)/(4) n + 12\leq n`

⇒
`(3)/(4) n \leq n - 12`

⇒
`(3)/(4) n - n \leq - 12`

⇒
`(3)/(4) n - (4)/(4)n \leq - 12`

⇒
`-(n)/(4) \leq - 12`

⇒
`-n\leq -36`

⇒
`n\geq 36` ( Because a>b ⇒ -a<-b )

Hence, the maximum number carry by the cable car = 36