You are buying two kinds of notebooks for school. A three-ring notebook costs $6, and a spiral notebook costs $3. You must have at least five notebooks. The cost of the notebooks can be no more than $24.
Which system of inequalities, along x>0 and y>0 would you use to solve the real-world problem?
To solve the given real-world problem, we need to set up a system of inequalities based on the given conditions.
Let x represent the number of three-ring notebooks and y represent the number of spiral notebooks.
According to the problem, we must have at least 5 notebooks. Therefore, the first inequality is:
x + y ≥ 5
Also, the cost of the notebooks can be no more than $24. We know that a three-ring notebook costs $6, and a spiral notebook costs $3. So the cost inequality can be written as:
6x + 3y ≤ 24
Finally, the given restrictions x > 0 and y > 0 indicate that we cannot have zero or negative numbers of notebooks.
Hence, the complete system of inequalities to represent the given real-world problem is:
x + y ≥ 5
6x + 3y ≤ 24
x > 0
y > 0
To solve the real-world problem described, we need to set up a system of inequalities. Let's assign variables to the unknown quantities:
Let x represent the number of three-ring notebooks.
Let y represent the number of spiral notebooks.
Now, let's analyze the information provided in the problem:
1. "You must have at least five notebooks."
This means that the total number of notebooks (x + y) should be greater than or equal to 5:
x + y ≥ 5
2. "A three-ring notebook costs $6, and a spiral notebook costs $3."
Let's consider the cost constraint. The total cost of the notebooks (6x + 3y) must be no more than $24:
6x + 3y ≤ 24
Additionally, you mentioned x > 0 and y > 0, which indicates that the number of notebooks must be positive. Hence, we have the following system of inequalities:
x + y ≥ 5
6x + 3y ≤ 24
x > 0
y > 0
This system of inequalities ensures that you have at least five notebooks, restricts the cost to be no more than $24, and ensures positive values for both types of notebooks.
If t = $6 and s = $3, and you buy 5 notebooks
3t + 2s ≤ $24
Do you want > 5 notebooks?