Math Problem Statement

In this number pyramid, each brick is the sum of the two bricks below it. Find the value of x.

Solution

To solve the pyramid, we note that each brick is the sum of the two bricks below it. The base of the pyramid is given as xx, 2x2x, and 3x3x. Let's compute step by step.

Step 1: The middle brick in the second row

The middle brick in the second row is the sum of the first two bricks in the bottom row: x+2x=3xx + 2x = 3x

Step 2: The right brick in the second row

The right brick in the second row is the sum of the last two bricks in the bottom row: 2x+3x=5x2x + 3x = 5x

Step 3: The top brick

The top brick is the sum of the two bricks in the second row: 3x+5x=8x3x + 5x = 8x

We are told the top brick is equal to 24. Therefore, we set up the equation: 8x=248x = 24

Step 4: Solve for xx

Divide both sides of the equation by 8: x=3x = 3

Final Answer:

The value of xx is 3.

Would you like further clarification or details? Here are 5 related questions to explore:

  1. How would the solution change if the top brick had a different value, like 30?
  2. Can we generalize the solution for any given values in the base row?
  3. What are the values of all the bricks in this specific pyramid?
  4. How does the pyramid structure relate to other number sequences, like Pascal's triangle?
  5. How can this problem be extended to a pyramid with more rows?

Tip: Always double-check your equations and alignments when working through pyramid problems—they build sequentially, so an error in one step affects all others.

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Math Problem Analysis

Mathematical Concepts

Algebra
Arithmetic
Number Pyramids

Formulas

Sum of two elements in a row: a + b = c

Theorems

Basic properties of arithmetic sums

Suitable Grade Level

Grades 6-8