Question

A semi-trailer truck stops at a weigh station before crossing over a bridge. The weight limit on the bridge is75,500 pounds. The cab (front) of the truck weighs 22,150 pounds, and the trailer (back) of the truck weighs11,300 pounds when empty. In pounds, how much cargo can the truck carry and still be allowed to cross the bridge?
Part I: Write an equation or inequality that models this situation. Let c be the cargo weight. Show your work.

)Part II: Solve the equation or inequality you wrote in Part I for c. What does this tell you about how much cargothe truck can carry and still be allowed to cross the bridge?

Answer 1

Part I

The weight of the truck without cargo is 22150+11300= 33450 pound
The weight of the cargo is given as $c$ and altogether with the weight of the truck, the sum must not exceed 75500

The inequality is given $33450+c \leq 75500$

Part II
$33450+c \leq 75500$
$c \leq 75500-33450$
$c \leq 42050$

Hence, the maximum weight allowed for the cargo is 42050 pounds