Respuesta :
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.
[tex]8t+7c=296[/tex]
[tex]8t=296-7c[/tex]
[tex]t=37-\frac{7c}{8}[/tex]
The number of trucks should be natural number.
Substitute c=0 in [tex]t=37-\frac{7c}{8}[/tex]
[tex]t=37-\frac{7(0)}{8}[/tex]
[tex]t=37[/tex]
Substitute c=8 in [tex]t=37-\frac{7c}{8}[/tex]
[tex]t=37-\frac{7(8)}{8}[/tex]
[tex]t=37-7[/tex]
[tex]t=30[/tex]
Substitute c=16 in [tex]t=37-\frac{7c}{8}[/tex]
[tex]t=37-\frac{7(16)}{8}[/tex]
[tex]t=37-14[/tex]
[tex]t=23[/tex]
Substitute c=24 in [tex]t=37-\frac{7c}{8}[/tex]
[tex]t=37-\frac{7(24)}{8}[/tex]
[tex]t=37-21[/tex]
[tex]t=16[/tex]
Substitute c=32 in [tex]t=37-\frac{7c}{8}[/tex]
[tex]t=37-\frac{7(32)}{8}[/tex]
[tex]t=37-28[/tex]
[tex]t=9[/tex]
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;
