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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

Respuesta :

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

[tex]\left \{ {{x+y=21} \atop {2x+4y=54}} \right.[/tex]

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:

[tex]\left \{ {{2(x+y=21)} \atop {2x+4y=54}} \right.  \\ \\\left \{ {{2x+2y=42} \atop {2x+4y=54}} \right.[/tex]

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

[tex]\left \{ {{2x+2y=42} \atop {-(2x+4y=54)}} \right.  \\ \\-2y=-12[/tex]

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.

shubhamchouhanvrVT

The number of bicycles is 15 and skateboards is 6.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

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.

x + y = 21

2x + 4y = 54

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:

2x + 2y = 42

2x + 4y = 54

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

Therefore, the number of bicycles is 15 and skateboards is 6.

To know more about an expression follow

https://brainly.com/question/723406

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