Write a real life situation that can be modeled by the inequality \large 3x+4y\le24.
To come up with a real-life situation that can be modeled by the inequality \(\large 3x+4y \leq 24\), let's break down the inequality and understand its components.
The inequality \(\large 3x+4y \leq 24\) represents a linear function, where \(x\) and \(y\) are variables, and 3 and 4 are coefficients associated with each variable. The sum of the products of the variables and coefficients is less than or equal to 24.
Now, let's consider a real-life situation that can be modeled using this inequality:
Imagine you have a limited amount of money to buy apples (\(x\)) and oranges (\(y\)) from a farmer's market. The price of each apple is $3, and the price of each orange is $4. You want to buy a combination of apples and oranges such that the total cost is less than or equal to $24.
In this scenario, the equation \(\large 3x+4y \leq 24\) comes into play. The inequality ensures that the sum of the product of the quantity of apples and their cost (\(3x\)) and the product of the quantity of oranges and their cost (\(4y\)) doesn't exceed $24. This inequality represents the constraint on the total cost of your purchase.
For example, if you decide to buy 4 apples (\(x = 4\)) and 3 oranges (\(y = 3\)), the total cost would be \(\large 3(4) + 4(3) = 12 + 12 = 24\), which exactly satisfies the inequality. However, if you tried to buy more apples and/or oranges, the total cost would exceed $24, violating the inequality.
Therefore, this real-life situation of buying apples and oranges subject to a budget constraint can be properly modeled using the inequality \(\large 3x+4y \leq 24\).