SOLUTION: 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 durin

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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
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
c for cars, b for busses

and you only want whole number coordinate pairs.

The greatest number of busses,



Greatest number of cars,


Cars x-axis, busses y-axis;
Identifying the points will be easier if done on gridded graph paper.

You could also try start at the x-intercept and count to each whole numbered point according to the slope. This would give (13,2) as a possible point for 13 cars and two busses; (10,4) is another; and you can keep going...
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
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 
Let number of buses be B, and number of cars, C

Then we get: 2C + 3B = 32

2C = 32 – 3B



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: , 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 ≥ 0 but < 11



This results in:

Collection for:  

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