Final Answer:
Hayley's method for calculating the total number of pieces of fruit is represented by the expression
where
denote the quantities of apples and oranges, respectively. As an example, with 4 apples and 6 oranges, the calculation would be
resulting in a total of 19 pieces of fruit.
Step-by-step explanation:
Hayley's method involves assigning coefficients to each fruit type and creating an expression to efficiently calculate the total quantity of fruit. In this case,
represents the contribution of apples, and
represents the contribution of oranges. The expression
ensures that the sum of these contributions is divided by 2 to obtain the total number of pieces of fruit.
Let's illustrate this with a numerical example: consider having 4 apples
) and 6 oranges
The calculation becomes
First, compute the contributions from each fruit type:
for apples and
for oranges.
Then, add these contributions:
Finally, divide the sum by 2:
Therefore, with 4 apples and 6 oranges, there are a total of 19 pieces of fruit.
The effectiveness of this method lies in its simplicity and adaptability to varying quantities of apples and oranges. By using coefficients, the expression provides a concise and clear way to calculate the total quantity without individually counting each piece, streamlining the process for efficient calculations in scenarios involving different quantities of apples and oranges.
Question:
Describe Hayley's method for calculating the total number of pieces of fruit using the expression (5x + 3y) / 2. Provide an example to illustrate the calculation. Explain the effectiveness of this method and how it simplifies the process of determining the total quantity of fruit in scenarios involving different quantities of apples (x) and oranges (y)?