Genesis goes apple picking. She has to pay $5.00 for a basket plus a certain rate per apple. She puts 10 apples in her basket, and the final cost is $7.50. Write a linear model to represent the situation. What is the amount per apple that Genesis has to pay? Enter your response as a whole number followed by a decimal and two digits.

Question

GPT-4o mini · Answer

To set up a linear model for the situation, let's define the variables involved:

Let $ x $ be the cost per apple.
The fixed cost for the basket is $5.00.
She picks 10 apples.

The total cost (C) can be expressed with the following formula: \[ C = \text{basket cost} + (\text{number of apples} \times \text{cost per apple}) \] Substituting the known values into the equation: \[ C = 5.00 + (10 \times x) \]

According to the problem, the total cost (C) is $7.50. Therefore, we can set up the equation: \[ 7.50 = 5.00 + (10 \times x) \]

To solve for $ x $, we first subtract the basket cost from both sides: \[ 7.50 - 5.00 = 10x \] \[ 2.50 = 10x \]

Next, divide both sides by 10 to solve for $ x $: \[ x = \frac{2.50}{10} = 0.25 \]

Thus, the cost per apple that Genesis has to pay is $ 0.25 $.

Finally, the answer as a whole number followed by a decimal and two digits is: \[ 0.25 \]