Question

hector collects rainwater in a large barrel that weighs 15 pounds. when there are 10 gallons of water in the barrel, the total weight of the barrel and the water is 98.4 pounds. when there are 20 gallons of water, the total weight is 181.8 pounds. which equation and graph match this situation? a. $y = 8.34x + 15$ weight of water and barrel

Explanation:

Step1: Find the weight of 1 gallon of water

First, we find the weight of the water alone when there are 10 gallons and 20 gallons. The barrel weighs 15 pounds. For 10 gallons, water weight is \(98.4 - 15 = 83.4\) pounds. For 20 gallons, water weight is \(181.8 - 15 = 166.8\) pounds. The rate (weight per gallon) is \(\frac{166.8 - 83.4}{20 - 10}=\frac{83.4}{10} = 8.34\) pounds per gallon.

Step2: Determine the equation

The total weight \(y\) (barrel + water) is the weight of the barrel (15 pounds) plus the weight of the water. The weight of the water is \(8.34x\) (where \(x\) is gallons of water). So the equation is \(y = 8.34x + 15\), which matches option A.

Answer:

A. \(y = 8.34x + 15\)