Question

.During a 4th of July weekend, 32 vehicles became trapped on the Sunshine Skyway Bridge while it was being repaved. A recent city ordinance decreed that only cars with 4 wheels and trucks with six wheels could be on the bridge at any given time. If there were 148 tires that needed to be replaced to due to damage, how many cars and trucks were involved in the incident?

Answer 1

can someone help me with the formula

Answer 2

or explain how to do it

Answer 3

Let x be the number of cars, and y be the number of trucks.
There are 32 vehicles on the bridge, so the number of cars plus the number of truck must be 32. In math language that means:
\[x+y = 32\]
Does that make sense?

Answer 4

so 32 cars = 148 tires

Answer 5

you're jumping ahead a little.
That equation i posted above isnt concerned about the tires, just the number of vehicles on the bridge.
Now we are going to look at the tires. Each car has 4 tires, so the number of car tires on the bridge is 4 times x, or 4x. Each truck as 6 tires, so the number of truck tires is 6 times y, or 6y. The total number of tires is 148 so in math terms we have:
\[4x+6y = 148\]

Answer 6

So now we have a system of equations: \[x+y = 32\]\[4x+6y = 148\]
solving this system will tell you how many cars and trucks there are.

Answer 7

okay but now for x+y=32 do you just pick your own numbers?

Answer 8

Picking numbers for the first equation could lead to the right answer, you would just have to check you answer in the second equation to see if it works. For example, if i thought the answer was: x = 30 y = 2, when I check it in the second equation i get:
4(30)+6(2) = 148
120+12 = 148
132 = 148
Which is wrong. so x = 30 and isnt the answer.

Answer 9

and y = 2*

Answer 10

Guess and Check is one method to solving these, but its almost like you have to get lucky. I recommend either substitution, or elimination.

Answer 11

okay.

Answer 12

http://www.jamesbrennan.org/algebra/systems/substitution_method.htm
This is a walk through on substitution.

Answer 13

This one is about elimination. While nice to know, your particular problem is better solved with substitution.
http://rachel5nj.tripod.com/NOTC/ssoewog2.html