A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 45 pounds each, and the small boxes weigh 25 pounds each. There are 115 boxes in all. If the truck is carrying a total of 4175 pounds in boxes, how many of each type of box is it carrying? Number of large boxes: Number of small boxes:

Let's break this puzzle down to find out how many large and small boxes are on the truck. We can define two variables: let \( x \) be the number of large boxes and \( y \) be the number of small boxes. We know that: 1. \( x + y = 115 \) (the total number of boxes) 2. \( 45x + 25y = 4175 \) (the total weight of the boxes) Now, we can solve these equations step by step. From the first equation, we can express \( y \) in terms of \( x \): \[ y = 115 - x \] Substituting this into the second equation gives: \[ 45x + 25(115 - x) = 4175 \] Now, distribute the \( 25 \): \[ 45x + 2875 - 25x = 4175 \] Combining the terms leads to: \[ 20x + 2875 = 4175 \] Subtracting \( 2875 \) from both sides yields: \[ 20x = 1300 \] Dividing by \( 20 \): \[ x = 65 \] Now substituting \( x \) back into the equation to find \( y \): \[ y = 115 - 65 = 50 \] So, the delivery truck is carrying 65 large boxes and 50 small boxes. Number of large boxes: 65 Number of small boxes: 50