Suppose you intend to spend no more than $60 buying books. Hardback books cost $12 and paperbacks cost $5. How many books of each type can you buy?
The inequality is
12H+5P ≤ 60
Many answers are possible, such as:
H=5, P=0, total=60
H=4, P=2, total=58
H=3, P=4, total=56
H=2, P=7, total=59
....
To find out how many books of each type can be bought without spending more than $60, we can use a system of equations.
Let's assume x represents the number of hardback books and y represents the number of paperback books.
The cost of each hardback book is $12, so the total cost of x hardback books is 12x dollars.
Similarly, the cost of each paperback book is $5, so the total cost of y paperback books is 5y dollars.
According to the given information, the total cost of all books is no more than $60.
Therefore, we can write the following equations:
12x + 5y ≤ 60 (equation 1)
x, y ≥ 0 (equation 2)
Now, we can solve this system of equations to determine the maximum number of books of each type that can be bought.
One way to solve this is by using trial and error or intuition. However, for a more systematic approach, let's graph the equation 12x + 5y = 60 to find the feasible region.
By rearranging equation 1, we have:
5y = 60 - 12x
y = (60 - 12x) / 5
Now, we can plot this equation on a coordinate plane with x and y axes.
By substituting different values of x and finding the corresponding y values, we can plot multiple points on the graph. Connecting these points will give us a line.
By observing the graph and noticing that x and y must be non-negative (equation 2), we can determine the feasible region, which is the area below or on the line, including the axes.
Next, we identify the points on this line that have whole number solutions (whole number values for x and y) since we are dealing with the number of books.
Upon identifying these points, we can calculate the maximum number of books of each type that can be bought while spending no more than $60.
As an AI bot, I am unable to provide visual graphs; however, you can plot the equation 12x + 5y = 60 on graph paper, or use software or online graphing tools to help you visualize the solution. Once you determine the feasible region, you can identify the whole number solutions to find the maximum number of books of each type that can be bought.