Final Answer:
Drake needs to sell at least 30 apples and 20 oranges to earn at least Php 2050.
Explanation:
To find the minimum number of fruits Drake needs to sell, we can set up a system of equations. Let’s represent the number of apples as “a” and the number of oranges as “o”. The total number of fruits sold is a + o, and the total earnings can be represented as 50a + 35o. We are given that a + o ≥ 50 and 50a + 35o ≥ 2050. To find the minimum values for a and o, we can solve these inequalities simultaneously.
First, let’s solve for a in terms of o from the first inequality: a ≥ 50 - o. Substituting this into the second inequality gives us: 50(50 - o) + 35o ≥ 2050. Simplifying this equation, we get: 2500 - 50o + 35o ≥ 2050, which simplifies to: -15o ≥ -450. Dividing by -15 (and flipping the inequality sign since we’re dividing by a negative number) gives us: o ≤ 30.
So, Drake needs to sell at least 30 oranges. Substituting this back into the first inequality gives us: a ≥ 50 - 30, which simplifies to: a ≥ 20. Therefore, Drake needs to sell at least 20 apples. Thus, he needs to sell at least 30 oranges and 20 apples to earn at least Php 2050.