We want to find out how much a treadmill bought by a fitness instructor costs. We can create a system of linear equations and then solve it using the Elimination Method to help us. Let's begin with a verbal model that represents the situation. Let the cost of a treadmill be x and the cost of an exercise bike be y.
From the exercise, we know that the fitness instructor bought 2 exercise bikes and 3 treadmills for a total of $ 2200 for the first gym. For the second gym, the instructor spent a total of $ 3000 on 3 exercise bikes and 4 treadmills. Keeping this in mind, let's create a system of equations.
3* x+ 2* y= 2200 & (I) 4* x+ 3* y= 3000 & (II)
Now that we have a system, we can solve it using the Elimination Method. Notice that no pair of like terms has the same or opposite coefficients. To solve the system by the Elimination Method, we will multiply Equation (I) by 3 and Equation (II) by 2 so that the y terms have the same coefficient. Let's do it!
Now we can subtract Equation (II) from Equation (I) to get an equation in only one variable, x. We also could have multiplied one of the equations by a negative number and then added them together. Since we want to solve the system for just the number of treadmills, x, we want to eliminate the y-variable.
