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.
Accepted Solution
A:
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;