A shipping company charges a $5 flat fee for a package, plus a fee based on the weight of the package. The company charges $1.50 per pound, plus an additional $0.50 for every pound over 5 pounds.
Jakob plans on sending a package that is over 5 pounds. He has $30 to spend on shipping. What is the maximum number of pounds that his package could be? Enter your answer as a decimal.
pounds
Let's assume that the package weighs x pounds.
The additional fee for every pound over 5 pounds is $0.50, so the fee for the additional pounds is 0.50 * (x - 5).
The total fee for the package is the sum of the $5 flat fee, the $1.50 per pound fee, and the additional fee for the additional pounds: $5 + $1.50x + 0.50(x - 5).
We know that Jakob has $30 to spend on shipping, so we can set up the equation:
$30 = $5 + $1.50x + 0.50(x - 5).
Simplifying the equation:
$25 = $2x + 0.50x - $2.50
$25 = $2.50x - $2.50
$27.50 = $2.50x
x = $27.50 / $2.50
x = 11.
Therefore, the maximum number of pounds that Jakob's package could be is 11.