Question

The average length of three tapes is 6800 feet. None of the tapes is less than 6400 feet. What is the greatest possible length of one of the other tapes?

• A. 6400
• B. 6800
• C. 7600
• D. 6700
• E.

Hint:

When working with averages, use the total sum and subtract the minimum values to find the maximum possible value for the remaining item.

Answer 1

The Correct Option is C

Step 1: Compute the total length of the three tapes. The given average length of the tapes is 6800 feet. Thus, the total length of all three tapes is: \[ \text{Total length} = 6800 \times 3 = 20400 \text{ feet}. \] Step 2: Establish the maximum allowable length for two tapes. Since one of the tapes has a length of 6400 feet, the combined length of the other two tapes must be: \[ 20400 - 6400 = 14000 \text{ feet}. \] Step 3: Minimize the sum of two tapes to maximize the third. To achieve the maximum possible length for one tape, the sum of the lengths of the other two tapes must be minimized. The smallest possible total length for these two tapes is when both are 6400 feet: \[ 6400 + 6400 = 12800 \text{ feet}. \] Step 4: Compute the maximum length of the longest tape. \[ \text{Length of the longest tape} = 20400 - 12800 = 7600 \text{ feet}. \] Thus, the maximum possible length of one tape is 7600 feet. s