Question

the total weight of a delivery truck is equal to the weight of the empty truck plus the weight of the packages. the truck weighs 8,200 lb when empty. write an equation that shows how to use the total weight of the truck to find the weight of the packages. show your work.

Explanation:

Step1: Define Variables

Let \( T \) be the total weight of the truck, \( E \) be the weight of the empty truck, and \( P \) be the weight of the packages. Given \( E = 8200 \) lb. The relationship is \( T=E + P \), so we can rearrange to solve for \( P \): \( P=T - E \). But if we assume we want to express total weight in terms of package weight, the equation is \( T = 8200+P \). If we need to find \( P \) when \( T \) is known, or \( T \) when \( P \) is known, we use this equation. For example, if we know the total weight, say \( T \) is given, then \( P=T - 8200 \).

Step2: Example Application (if total weight is given)

Suppose the total weight \( T \) is, for example, 10000 lb. Then \( P=T - 8200=10000 - 8200 = 1800 \) lb. But the key equation is \( T=8200 + P \) (or \( P=T - 8200 \)) to relate total weight, empty weight, and package weight.

Answer:

The equation relating total weight (\( T \)), empty weight (\( E = 8200 \) lb), and package weight (\( P \)) is \( T=8200 + P \) (or \( P=T - 8200 \)) to find the weight of the packages.