Question

mckenna and lara work for their uncle eddie, who repairs skateboards and bicycles. uncle eddie is leaving for a vacation to the amazon. he asks the girls to order 54 new new wheels for the 21 skateboards and bicycles in his repair shop. how many bicycles and how many skateboards are in uncle eddie's shop? how many bicycles and how many skateboards are in the shop? show your work

Answer 1

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

$\left \{ {{x+y=21} \atop {2x+4y=54}} \right.$

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:

$\left \{ {{2(x+y=21)} \atop {2x+4y=54}} \right. \\ \\\left \{ {{2x+2y=42} \atop {2x+4y=54}} \right.$

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

$\left \{ {{2x+2y=42} \atop {-(2x+4y=54)}} \right. \\ \\-2y=-12$

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.