![]() ![]() (six bananas) she will pay twice the price ($8). If Peter buys two apples and three bananas for $4, it makes sense that if Nadia buys twice as many apples (four apples) and twice as many bananas ![]() Looking at the problem again, we can see that we were given exactly the same information in both statements. Let's solve this system by multiplying the first equation by -2 and adding the two equations: Let's say is the cost of one apple and is the cost of one banana. We must write two equations: one for Peter's purchase and one for Nadia's purchase. How much does one banana and one apple costs? Nadia buys four apples and six bananas for $8 from the same store. Peter buys two apples and three bananas for $4. This means that the system is inconsistent. Let's solve this system by substituting the second equation into the first equation: The system of equations that describes this problem is: Once again, we'll call the number of movies you rent and the total cost of renting movies for a year. Now let's see how this works algebraically. The lines on a graph that describe each option have different intercepts - namely 30 for Movie House and 15 for Flicks for Cheap - but the same slope: 3 dollars per movie. It should already be clear to see that Movie House will never become the better option, since its membership is more expensive and it charges the same amount per movie as Flicks for Cheap. Flicks for Cheap charges an annual membership of $15 and charges $3 per movie rental. Movie House charges an annual membership of $30 and charges $3 per movie rental. Two movie rental stores are in competition. Real-World Application: Comparing Options The previous problem so that this is the case. From the previous explanation, we can conclude that the lines will not intersect if the slopes are the same (and the intercept is different). Now let's look at a situation where the system is inconsistent. The lines cross because the price of rental per movie is different for the two options in the problem In this case, the slopes of the lines represent the price of a rental per movie. In other words, the lines are not parallel Remember that for a consistent system, the lines that make up the system intersect at single point. This example shows a real situation where a consistent system of equations is useful in finding a solution. You would have to rent 30 movies per year before the membership becomes the better option. Substitute the second equation into the first one: Since each equation is already solved for, we can easily solve the system with substitution. ![]() Now we need to find the exact intersection point. For the membership option the rental fee is, since you would pay $2 for each movie you rented įor the no membership option the rental fee is, since you would pay $3.50 for each movie you rented. ![]() The flat fee is the dollar amount you pay per year and the rental fee is the dollar amount you pay when you rent a movie. We'll call the number of movies you rent and the total cost of renting movies for a year. The choices are "membership" and "no membership". Since there are two different options to consider, we can write two different equations and form a system. Let's translate this problem into algebra. Rent before the membership becomes the cheaper option? Customers can pay a yearly membership of $45 and then rent each movie for $2 or they can choose not to pay the membership fee and rent each movie for $3.50. The movie rental store CineStar offers customers two choices. Real-World Application: Yearly Membership ![]()
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