Q: The average wages of a worker during a fortnight comprising of 15 consecutive working days was $90 per day. During the first 7 days, his average wage was $87 per day and the average wage during the last 7 days was $92 per day. What was his wage on the 8th day? Answer Choices: (A) $83 (B) $92 (C) $90 (D) $97 (E) $104 A: Let’s first understand the problem, extract relevant variables and their corresponding numerals, and make a complete plan. Then, let’s carry out the plan, calculate intermediate variables (pay attention to correct numerical calculation and commonsense), solve the problem step by step, and show the answer.
Plan:
- We are given that the total number of working days in the fortnight is 15.
- We also know that the average wage for the entire fortnight was $90 per day.
- Additionally, we have information about the average wages for the first 7 days (92).
- To find the wage on the 8th day, we need to use these averages along with some calculations.
Calculations:
- First, let's calculate the total wage earned during the first 7 days: Total wage = Average wage x Number of days => Total wage = 609
- Similarly, let's calculate the total wage earned during the last 7 days: Total wage = Average wage x Number of days => Total wage = 644
- Now, let's add up the total wages from both periods: Total wage = 644 = $1253
- Since there were 15 working days in total, we can now divide the sum of the two periods by 15 to get the average wage for the whole fortnight: Average wage = 83.53
- However, this average wage doesn't match the given average wage of $90 per day. Therefore, our initial assumption must be incorrect.
- Let's reconsider our approach. Instead of using the average wages for each period directly, let's assume that the worker worked at a constant rate throughout the fortnight. This means that he earned the same amount on every single day.
- If we denote the daily wage as W, then the total wage earned during the first 7 days would be: Total wage = W x 7
- And the total wage earned during the last 7 days would be: Total wage = W x 7
- Adding these together gives us the total wage earned during the entire fortnight: Total wage = 2W x 7 = 14W
- Dividing this by 15 (since there were 15 working days in total) gives us the average wage for the whole fortnight: Average wage = 14W / 15
- Setting this equal to the given average wage of 90
- Solving for W, we get: W = 97.14
Final answer: His wage on the 8th day was $97.14.
Model: meta-llama/Llama-3.3-70B-Instruct ·
Generated content may be inaccurate
or false.