Answer
a) yes; no
b) 72 in. or 6 ft
Work Step by Step
a) We find the girth of the package that is 6 in. wide by plugging the values into the formula:
$L + 2(x+y) \leq 108$
$60 + 2(6 + 8) \leq 108$
$60 + 28 \leq 108$
$88 \leq 108$
Because 88 is less than 108, it is accepted.
We then find the girth of the package that is 4 in. wide by plugging the values into the formula:
$L + 2(x+y) \leq 108$
$48+ 2(24 + 24) \leq 108$
$48 + 96 \leq 108$
$144 \leq 108$
Since this is not true, it will not be accepted.
b) For the largest value of L, we want the total girth to be equal to 108. Therefore, plug these values into an equation and solve for L:
$L + 2(9 + 9) = 108$
$L + 36 = 108$
$L = 72$
The largest possible length is 72 inches, which can be converted into 6 ft.
