Answer
Part A:
Package that is 6 in. wide, 8 in. deep, and 5 ft long would be accepted.
Package that measures 2 ft by 2 ft by 4 ft would not be accepted.
Part B:
The greatest acceptable length for a package that is 9 inches wide and 9 inches deep is 72 inches.
Work Step by Step
Given formula: L + 2(x+y) $\leq$ 108 inches
Things to keep in mind:
L represents the length (how long it is)
x and y represent the girth (how wide and deep it is)
Our unit is inches, so at times we will convert from feet to inches.
Part A:
Will a package 6 inches wide, 8 inches deep, and 5 feet long be accepted?
To be accepted the measurements must $\leq$ 108 inches.
6 inches wide and 8 inches deep represent x and y, 5 feet long represents L.
Since our unit is inches, we have to covert the 5 feet to inches.
Conversion: 1 foot equals 12 inches, so 5 feet is 60 inches.
Putting everything into our given formula yields:
60 + 2 (6 + 8) $\leq$ 108 ?
60 + 2 (14) $\leq$ 108 ?
60 + 28 $\leq$ 108 ?
88 $\leq$ 108 ✓
Therefore, a package with these dimensions would be accepted.
Will a package 2 feet wide, 2 feet deep, and 4 feet long be accepted?
We must convert from feet to inches:
2 feet is 24 inches, and 4 feet is 48 inches
Putting this into the formula yields:
48 + 2 (24 + 24) $\leq$ 108 ?
48 + 2 (48) $\leq$ 108 ?
48 + 96 $\leq$ 108 ?
144 $\leq$ 108 ✗
This is false because 144 is greater than 108.
Therefore, a package with these dimensions would not be accepted.
Part B:
What is the greatest acceptable length for a package that is 9 inches wide, and 9 inches deep?
Putting the known dimensions into our formula yields:
L + 2 (9+9) $\leq$ 108
L + 2(18) $\leq$ 108
L + 36 $\leq$ 108
L $\leq$ 72
Therefore, the length must be less than or equal to 72 inches.
In other words, the greatest acceptable length for a package with the given dimensions is 72 inches.
