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

Answer:

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;

Step-by-step 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.

$8t+7c=296$

$8t=296-7c$

$t=37-\frac{7c}{8}$

The number of trucks should be natural number.

Substitute c=0 in $t=37-\frac{7c}{8}$

$t=37-\frac{7(0)}{8}$

$t=37$

Substitute c=8 in $t=37-\frac{7c}{8}$

$t=37-\frac{7(8)}{8}$

$t=37-7$

$t=30$

Substitute c=16 in $t=37-\frac{7c}{8}$

$t=37-\frac{7(16)}{8}$

$t=37-14$

$t=23$

Substitute c=24 in $t=37-\frac{7c}{8}$

$t=37-\frac{7(24)}{8}$

$t=37-21$

$t=16$

Substitute c=32 in $t=37-\frac{7c}{8}$

$t=37-\frac{7(32)}{8}$

$t=37-28$

$t=9$

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;