fit binding constants k for these three data sets. what are the uncertainties on your three fitted binding constants?

The correct answer is:

15 bicycles and 6 skateboards.

Explanation:

Let x represent the number of bicycles and y represent the number of skateboards.  The first equation in our system is then

x+y = 21, since there are 21 total items in the shop.

Each bicycle has 2 tires and each skateboard has 4; this gives us the equation

2x+4y=54 (because they are ordering 54 tires).

This makes our system

We will use elimination to solve this; we first need one of the variables to have the same coefficient in both equations.  We will make x the same, and we will do this by multiplying the first equation by 2:

Now we will subtract the second equation from the first one:

Divide both sides by -2:

-2y/-2 = -12/-2

y = 6

There were 6 skateboards.  Substituting this into the first equation,

x+6 = 21

Subtract 6 from each side:

x+6-6 = 21-6

x = 15

There were 15 bicycles.