A playground is filled with bikes and wagons. If there are 24 bikes and wagons in total and 80 wheels altogether, how many bikes are there? How many wagons?

There are 8 bikes and 16 wagons.

Step-by-step explanation:

We will use a system of equations to solve this problem.

Step 1. First, we assign variables to represent the unknowns.

Step 2. Then we will write two equations.

Step 3. Finally, we will solve the system of equations and will answer the questions.

Step 1. First, we assign variables to represent the unknowns.

Let the number of bikes = b.

Let the number of wagons = w.

Step 2. Then we will write two equations.

The first equation deals with the numbers of bikes and wagons.

The total number of bikes and wagons is 24.

b + w = 24

4y - 36 = - 12x

The second equation deals with the numbers of wheels.

The number of wheels on a bike is 2, so b number of bikes have 2b number of wheels.

The number of wheels on a wagon is 4, so w number of wagons have 4w number of wheels.

The total number of wheels is 2b + 4w. We are told there are a total of 80 wheels, s we get the second equation.

2b + 4w = 80

Now we have a system of equations.

b + w = 24

2b + 4w = 80

Step 3. Finally, we will solve the system of equations and will answer the questions.

Multiply both sides of the first equation by - 2.

-2b - 2w = - 48

2b + 4w = 80

Add the equations.

2w = 32

w = 16

b + w = 24

b + 16 = 24

b = 8

There are 8 bikes and 16 wagons.