Question 995470
A toll collector on a highway receives $2 for cars and $3 for busses. At the end of a 1-hour period, she collected $32. How many cars and busses passed through the toll booth during that period? List all possible answers 
<pre>Let number of buses be B, and number of cars, C
Then we get: 2C + 3B = 32
2C = 32 – 3B
{{{C = (32 - 3B)/2}}}
C and B MUST be INTEGERS

B or number of buses CANNOT be 11, as this would yield a value of "- 1" for the number of cars

Also, based on the above equation: {{{C = (32 - 3B)/2}}}, B or number of buses CANNOT be an ODD INTEGER, so B or number of buses MUST be an EVEN INTEGER value that’s < 11 

Therefore, number of buses that she collected for: All POSITIVE EVEN INTEGERS that are &#8805; 0 but < 11

This results in:
Collection for: {{{highlight_green(system(matrix(6,5,
0,buses,and,16,cars_OR,
2,buses,and,13,cars_OR,
4,buses,and,10,cars_OR,
6,buses,and,7,cars_OR,
8,buses,and,4,cars_OR,
10,buses,and,1,car)))}}}