Gissela, Gordy, and Gary are truck drivers. Gissela has a truck large enough to haul 4,000 pounds of gravel. Gordy's truck can haul 800 pounds more than Gissela's truck. And when Gary brings his truck and joins Gissela and Gordy, the three trucks combined can haul a total of 11,600 pounds of gravel. How many pounds of gravel can Gary's truck carry?

Answer: Gary's truck can carry 2800 pounds of gravel.

Step-by-step solution

Step 1: Define variables for each truck's capacity

To make the problem easier to solve, we assign variables to represent the carrying capacity of each person's truck. This helps us set up equations based on the information given.

Step 2: Determine Gissela's truck capacity

The problem states directly that Gissela's truck can haul 4,000 pounds of gravel. We record this known value.

Step 3: Calculate Gordy's truck capacity

Gordy's truck can haul 800 pounds more than Gissela's truck. We add 800 to Gissela's capacity to find Gordy's truck capacity. So, $4000 + 800 = 4800$ pounds.

Step 4: Set up an equation for the combined capacity

The problem states that the three trucks combined can haul a total of 11,600 pounds. We write this as an equation involving the sum of their individual capacities.

Step 5: Substitute known values into the combined capacity equation

Now we substitute the known capacities for Gissela's ( $G_A = 4000$ ) and Gordy's ( $G_O = 4800$ ) trucks into the combined capacity equation. This leaves only Gary's capacity as an unknown.

Step 6: Solve for Gary's truck capacity

First, we add the known capacities: $4000 + 4800 = 8800$ . Then, to find Gary's truck capacity ( $G_Y$ ), we subtract this sum from the total combined capacity: $11600 - 8800 = 2800$ . Thus, Gary's truck can carry 2800 pounds of gravel.

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