Bernie counted the cars and motorcycles that passed his house in 45 minutes. He counted 29 vehicles and 82 tires. How many motorcycles passed his house?

6

10

12

17

Question

Bernie counted the cars and motorcycles that passed his house in 45 minutes. He counted 29 vehicles and 82 tires. How many motorcycles passed his house?

 6

 10

 12

 17

johnweldon1993 · Answer

Well you know that in total...29 vehicles passed his house...so

c + m = 29

We also know that cars have 4 wheels and motorcycles have 2 wheels...and there were a total of 82 tires...so

4c + 2m = 82

Now can you solve the system of equations?

anonymous · Answer

6

johnweldon1993 · Answer

No don't just guess...

c + m =29
4c + 2m = 82

We want to solve for how many motorcycles passed by his house...so lets solve our first equation for 'c'

c + m = 29

How would we solve this for 'c'...?

anonymous · Answer

suub oth sidees

johnweldon1993 · Answer

Subtract what from both sides?

anonymous · Answer

29

johnweldon1993 · Answer

Not quite...we want to isolate 'c' on the left side....so we would subtract 'm' from both sides...what do we get when we do this?

johnweldon1993 · Answer

c + m = 29
    -m      -m

c = 29 - m   right?

anonymous · Answer

yup

johnweldon1993 · Answer

Now that we know what 'c' equals....we can use it to solve for 'm' in the second equation...

4c + 2m = 82

We know that 'c' = 29 - m...so replace it

4(29 - m) + 2m = 82

now simplify that...can you?

johnweldon1993 · Answer

*hint* distribute the 4 into the parenthesis