Questions: 2. A fruit basket contains the same number of apples and pears. If Eric eats 5 apples and 1 pear, there will be twice as many pears as apples. How many pears remain in the basket?

Solution Steps

To solve this problem, we need to set up an equation based on the given conditions. Let the initial number of apples and pears be \( x \). After Eric eats 5 apples and 1 pear, the number of apples becomes \( x - 5 \) and the number of pears becomes \( x - 1 \). According to the problem, the number of pears is twice the number of apples after Eric eats them. We can set up the equation \( x - 1 = 2(x - 5) \) and solve for \( x \). Once we find \( x \), we can determine the number of pears remaining in the basket.

Let \( x \) be the initial number of apples and pears in the basket. After Eric eats 5 apples and 1 pear, the number of apples becomes \( x - 5 \) and the number of pears becomes \( x - 1 \). According to the problem, the number of pears is twice the number of apples, leading to the equation: \[ x - 1 = 2(x - 5) \]

Expanding the equation gives: \[ x - 1 = 2x - 10 \] Rearranging this leads to: \[ -1 + 10 = 2x - x \] Thus, we find: \[ x = 9 \]

The initial number of pears is \( x = 9 \). After Eric eats 1 pear, the number of pears remaining is: \[ 9 - 1 = 8 \]

Final Answer