Question

A toll collector on a highway receives ​$8 for trucks and ​$7 for cars. At the end of a 33​-hour ​period, she collected ​$296. How many trucks and cars passed through the toll booth during that​ period? List all possible solutions.

Answer 1

The required list is: 0 car and 37 truck; 8 car and 30 truck; 16 car and 23 truck; 24 car and 16 truck; 32 car and 9 truck;

Explanation:

Consider the provided information.

A toll collector on a highway receives ​$8 for trucks and ​$7 for cars, at the end she collected ​$296.

Let t represents the number of trucks and c represents the number of cars pass through highway.

`8t+7c=296`

`8t=296-7c`

`t=37-(7c)/(8)`

The number of trucks should be natural number.

Substitute c=0 in
`t=37-(7c)/(8)`

`t=37-(7(0))/(8)`

`t=37`

Substitute c=8 in
`t=37-(7c)/(8)`

`t=37-(7(8))/(8)`

`t=37-7`

`t=30`

Substitute c=16 in
`t=37-(7c)/(8)`

`t=37-(7(16))/(8)`

`t=37-14`

`t=23`

Substitute c=24 in
`t=37-(7c)/(8)`

`t=37-(7(24))/(8)`

`t=37-21`

`t=16`

Substitute c=32 in
`t=37-(7c)/(8)`

`t=37-(7(32))/(8)`

`t=37-28`

`t=9`

Hence, the required list is: 0 car and 37 truck; 8 car and 30 truck; 16 car and 23 truck; 24 car and 16 truck; 32 car and 9 truck;