Question

Two block structures have the same total height. One structure is made of 14 blocks each with a height of h inches. The other structure is made with a base block that is 24 inches high and 11 additional blocks each with a height h inches. Write and solve an equation to find the height h of each of these blocks.

Answer 1

By setting up an equation with the total heights of the two block structures, we can solve for the height h of the blocks. After simplifying the equation, we find that the height h of each block, excluding the base block of the second structure, is 8 inches.

Step-by-step explanation:

To find the height h of the blocks in two structures that have the same total height, we can set up an equation. The first structure uses 14 blocks each with a height h inches, giving us a total height of 14h. The second structure has a base block of 24 inches and also uses 11 additional blocks each of height h, making its total height 24 + 11h. Since the structures have the same total height, we can equate their total heights:

14h = 24 + 11h

To solve for h, we subtract 11h from both sides, which yields 3h = 24. Dividing both sides by 3 gives us h = 8. Therefore, the height of each block in both structures, excluding the base block of the second structure, is 8 inches.