GMAT Practice Question: A certain work plan for September requires that a work team, working every day, produce an...
Question
A certain work plan for September requires that a work team, working every day, produce an average of 200 items per day. For the first half of the month, the team produced an average of 150 items per day. How many items per day must the team average during the second half of the month if it is to attain the average daily production rate required by the work plan?
- 225
- 250
- 275
- 300
- 350
Topics: word problems, linear equations, mean, rates, weighted averages
Solution
Step 1
We name x as the average items per day in the second half of the month.
x = \text{average items per day in the second half of the month}
Step 2
We find the total items needed for the month.
\text{Total items} = 200 \times 30 = 6000
Step 3
We find the items produced in the first 15 days.
\text{First half items} = 150 \times 15 = 2250
Step 4
We find how many items are needed in the second half by subtracting.
\text{Remaining items} = 6000 - 2250 = 3750
Step 5
We express the second half total as x times 15 days.
x \times 15 = 3750
Step 6
We solve for x by dividing both sides by 15.
x = \frac{3750}{15} = \frac{3000}{15} + \frac{750}{15} = \frac{\cancel{15} \times 200}{\cancel{15}} + \frac{\cancel{15} imes 50}{\cancel{15}} = 200 + 50 = 250
Answer
250
