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

Algebra ->  Probability-and-statistics -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
c for cars, b for busses

2c%2B3b=32 and you only want whole number coordinate pairs.

The greatest number of busses, 3b=32
b=32%2F3=10%262%2F3
highlight_green%28b=10%29

Greatest number of cars, 2c=32
highlight_green%28c=16%29

Cars x-axis, busses y-axis;
Identifying the points will be easier if done on gridded graph paper.
graph%28300%2C300%2C-2%2C18%2C-2%2C18%2C-2x%2F3%2B32%2F3%29
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) About Me  (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+=+%2832+-+3B%29%2F2

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+=+%2832+-+3B%29%2F2, 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: