Answer:
There are 8 bikes and 16 wagons.
Step-by-step explanation:
<em>We will use a system of equations to solve this problem.</em>
<em>Step 1. First, we assign variables to represent the unknowns.</em>
<em>Step 2. Then we will write two equations.</em>
<em>Step 3. Finally, we will solve the system of equations and will answer the questions.</em>
<em>Step 1. First, we assign variables to represent the unknowns.</em>
Let the number of bikes = b.
Let the number of wagons = w.
<em>Step 2. Then we will write two equations.</em>
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
<em>Step 3. Finally, we will solve the system of equations and will answer the questions.</em>
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.