During a weight - lifting routine, an athlete calculates the totla amount of weight moved while performing a certain exercise by multiplying the amount of weight per lift by the number of lifts. On Wednesday, the weight per lift was 20 percent greater than the weight per lift on Monday, while the number of lifts was 25 percent fewer than the number of lifts performed on Monday. On Friday, the weight per lift was 25 percent greater than the weight per lift on Wednesday, while the number of lifts was 40 percent fewer than the number of lifts performed on Wednesday. The total weight moved by the athlete while performing the exercise on Monday was approximately what percent greater than the total weight she moves while performing the exercise on Friday ?

Options

A. `15%`
B. `33%`
C. `48%`
D. `50%`

Explanation

To solve the problem step by step, we will define the variables and calculate the total weight moved on Monday and Friday, then find the percentage difference.

### Step 1: Define Variables
Let:
- Weight per lift on Monday = \( W \)
- Number of lifts on Monday = \( N \)

### Step 2: Calculate Weight and Lifts on Wednesday
On Wednesday:
- Weight per lift = \( W + 20\% \text{ of } W = W + 0.2W = 1.2W \)
- Number of lifts = \( N - 25\% \text{ of } N = N - 0.25N = 0.75N \)

### Step 3: Calculate Total Weight Moved on Monday
Total weight moved on Monday = Weight per lift × Number of lifts
\[ \text{Total weight on Monday} = W \times N = WN \]

### Step 4: Calculate Weight and Lifts on Friday
On Friday:
- Weight per lift = \( 1.2W + 25\% \text{ of } 1.2W = 1.2W + 0.25 \times 1.2W = 1.2W + 0.3W = 1.5W \)
- Number of lifts = \( 0.75N - 40\% \text{ of } 0.75N = 0.75N - 0.4 \times 0.75N = 0.75N - 0.3N = 0.45N \)

### Step 5: Calculate Total Weight Moved on Friday
Total weight moved on Friday = Weight per lift × Number of lifts
\[ \text{Total weight on Friday} = 1.5W \times 0.45N = 0.675WN \]

### Step 6: Calculate the Difference in Total Weight Moved
Difference in total weight moved = Total weight on Monday - Total weight on Friday
\[ \text{Difference} = WN - 0.675WN = 0.325WN \]

### Step 7: Calculate the Percentage Difference
To find what percent greater the total weight moved on Monday is compared to Friday:
\[ \text{Percentage} = \left( \frac{\text{Difference}}{\text{Total weight on Friday}} \right) \times 100 \]
\[ \text{Percentage} = \left( \frac{0.325WN}{0.675WN} \right) \times 100 \]
\[ \text{Percentage} = \left( \frac{0.325}{0.675} \right) \times 100 \approx 48.15\% \]

### Final Answer
The total weight moved by the athlete while performing the exercise on Monday is approximately **48.15% greater** than the total weight moved on Friday.