It appears that the specific values for the fraction of the box that Beth had initially and the percentage of the candy she ate are missing from the question. Without these values, we cannot provide a numeric answer. However, I will describe a general approach on how to solve this type of problem using a fraction model and writing an equation once the specific fractions are known.
Step 1: Identify the Initial Fraction
First, determine the initial fraction of the box of candy Beth had. This will be represented as a fraction, such as \(\frac{x}{y}\), where “x” represents the part of the box Beth had and “y” represents the whole box.
Step 2: Identify the Percentage Eaten
Next, we need to know the percentage of the candy that Beth ate. This will be a number \(P\), which we convert into a fraction by dividing by 100 (because percentages are out of 100).
Step 3: Draw a Fraction Model
Then we can draw a fraction model to help visualize the problem. The fraction model will consist of a rectangle that represents the entire box of candy, divided into "y" equal parts (as determined by the denominator of the initial fraction). We would then shade "x" parts to represent the fraction of the box Beth had initially. After that, to model the percentage Beth ate, we would shade "P" percent of the "x" shaded parts, signaling the amount of candy eaten.
Step 4: Write the Equation
We can calculate the fraction of the candy that Beth ate in terms of the initial fraction. Multiply the initial fraction (\(\frac{x}{y}\)) by the percentage (expressed as a fraction, which is \(P/100\)):
Fraction eaten = \(\frac{x}{y} * \frac{P}{100}\)
To find out how much candy Beth has left, we subtract the fraction eaten from the initial fraction:
Fraction left = Initial fraction - Fraction eaten
Fraction left = \(\frac{x}{y} - \left(\frac{x}{y} * \frac{P}{100}\right)\)
Step 5: Solve for the Fraction Left
To solve for the fraction left, we perform the subtraction:
Fraction left = \(\frac{x}{y} - \frac{xP}{100y}\)
Step 6: Find the Fraction to Refill
To refill the box, Beth would need to replace the same amount of candy that she ate, which is the fraction eaten (calculated in Step 4):
Fraction to refill = Fraction eaten
Step 7: Final Answer
Once both the initial fraction and the percentage are known, we can use this process to get a numeric fraction for how much candy Beth has left and how much she would need to refill.
For example, if Beth originally had 1/2 of the box and ate 25% of her portion, the fraction left would be:
Fraction left = \(\frac{1}{2} - \left(\frac{1}{2} * \frac{25}{100}\right)\)
Fraction left = \(\frac{1}{2} - \frac{1}{8}\)
Fraction left = \(\frac{4}{8} - \frac{1}{8}\)
Fraction left = \(\frac{3}{8}\)
So Beth has 3/8 of the box left. The fraction she would need to refill to make the box whole again would be 1/8, since that's the part she ate.
