The ACT® Math Test often asks students to "model average" at least once a test. They're seldom going to say "model the average." Instead, they're going to give you a long word problem, without once using the term model the average. That's because this is the technique you'll use to solve most of the world problems involving average.
Consider This Example
Teddy has the following test scores: 82, 91, 74, 90, 80. Coach says he needs to maintain an 84 average to keep playing. What must Teddy score on his next test to have an 84 average?
This question might seem technically complex at first. The way it's asked is typical of the way ACT® Math logic works: take information from one domain and apply it to another. In this case, the ACT® wants you to take probability and add simple algebra. We could rewrite the question as:
= 84
Then all we have to do is solve for .
Multiply both sides by 6 to eliminate the denominator:
Calculate :
Substitute the result back into the equation:
Add the known numbers:
Substitute this sum back into the equation:
Solve for :
Practice Section
Question:
Laura is a sales representative. Her sales for the first five months of the year are as follows (in thousands of dollars): 35, 42, 38, 50, 45. Her manager says she needs to maintain an average of \$45,000 in sales per month to receive a bonus. What must Laura sell in the sixth month to achieve an average of \$45,000?
- A) 55
- B) 60
- C) 65
- D) 70
- E) 75
Click for the Answer
Correct Answer: C) 65
Explanation:
- Set up the equation for the average:
- Multiply both sides by 6 to eliminate the denominator:
- Add the known sales:
- Substitute the sum back into the equation:
- Solve for :
Explanation of Answer Choices:
- A) 55: Incorrect. This is below the required sales amount.
- B) 60: Incorrect. This is slightly below the required sales amount.
- C) 65: Correct. This maintains the required average.
- D) 70: Incorrect. This is above the required sales amount.
- E) 75: Incorrect. This is significantly above the required sales amount.
Question:
John is working on a project with the following completion times for the first five tasks (in hours): 5, 6, 4, 7, 6. His supervisor says he needs to maintain an average of 6 hours per task to meet the deadline. How much time can John take to complete the sixth task to maintain the average of 6 hours?
- A) 5 hours
- B) 6 hours
- C) 7 hours
- D) 8 hours
- E) 9 hours
Click for the Answer
Correct Answer: D) 8 hours
Explanation:
- Set up the equation for the average:
- Multiply both sides by 6 to eliminate the denominator:
- Add the known times:
- Substitute the sum back into the equation:
- Solve for :
Explanation of Answer Choices:
- A) 5 hours: Incorrect. This is below the required time.
- B) 6 hours: Incorrect. This is below the required time.
- C) 7 hours: Incorrect. This is below the required time.
- D) 8 hours: Correct. This maintains the required average.
- E) 9 hours: Incorrect. This is above the required time.