30 min on the elliptical trainer and 10 min on the stationary bike.
Practice makes perfect
We are told that we have a total of 40 minutes to exercise. If we let t be the time we exercise on the elliptical trainer and b be the time we exercise on the stationary bike, we can write an equation to represent the situation.
40=t+b
We can rearrange this equation, so it will be easier to plot it later.
b=- t+40We are also told that we burn 8 calories per minute on the elliptical trainer and 6 calories per minute on the stationary bike. With this information, we can calculate how much calories you will burn in total.
Verbal expression
Algebraic expression
Calories burnt on the elliptical trainer per minute
8
Time spent on the elliptical trainer
t
Total calories burnt on the elliptical trainer
8t
Calories burnt on the stationary bike per minute
6
Time spent on the stationary bike
b
Total calories burnt on the stationary bike
6b
Total calories burnt on both machines
8t+6b
Let's build an equation that compares the total calories burnt with the given goal of 300 calories.
300=8t+6b
Isolating b will help us graph this equation.
From the graph, we can see that the solution, or point of intersection, to this system of linear equations is the point (30,10). However, we should check the point by substituting it into the equations. Let's start with the first one.
Since both equations hold true, the point (30,10) is a solution. This means that we should exercise 30 minutes on the elliptical trainer and 10 minutes on the stationary bike.
