Final answer:
Diana will make $15,120 by selling the cucumbers from her backyard garden.
Step-by-step explanation:
To find out how much money Diana will make, we first need to calculate the number of cucumbers she can grow in her garden. Her garden is 42 square feet in total, and she can grow 1 cucumber every 72 square inches. So, we divide the total garden area by the area needed to grow 1 cucumber:
42 square feet / (1 square foot / 144 square inches) = 42 * 144 cucumbers = 6,048 cucumbers.
Next, we need to calculate the total revenue Diana will make by selling the cucumbers. She sells each cucumber for $2.50. So the total revenue is:
6,048 cucumbers * $2.50/cucumber = $15,120.
Therefore, Diana will make $15,120 by selling the cucumbers from her backyard garden.