Math Problem Statement

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

Solution

The problem is asking to find the value of xx in a number pyramid, where each brick is the sum of the two bricks directly below it. Here’s how we can set up the equations based on the given pyramid structure:

We have:

  • Top brick: 35
  • Middle bricks: Unknown values
  • Bottom bricks: 2x2x, xx, and 3x3x

According to the rule of the pyramid:

  1. The two middle bricks must sum to give 35. These middle bricks are the sums of the bottom pairs:

    • The left middle brick is the sum of 2x2x and xx, so it equals 2x+x=3x2x + x = 3x.
    • The right middle brick is the sum of xx and 3x3x, so it equals x+3x=4xx + 3x = 4x.
  2. The top brick is the sum of the two middle bricks: 3x+4x=353x + 4x = 35 Simplifying: 7x=357x = 35 Solving for xx: x=357=5x = \frac{35}{7} = 5

Thus, the value of xx is 5\boxed{5}.

Would you like any more details or explanations on this solution?

Here are 5 related questions you can explore:

  1. What would the bottom numbers be if x=7x = 7?
  2. How do number pyramids help in understanding algebraic relationships?
  3. Can you build a larger number pyramid with a similar rule and solve it?
  4. How does the concept of solving simultaneous equations relate to this problem?
  5. How can we generalize this pyramid approach for different shapes?

Tip: Always double-check if you need to distribute or simplify equations before solving for the variable.

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Math Problem Analysis

Mathematical Concepts

Algebra
Arithmetic Sequences
Equations

Formulas

Sum of terms formula: top brick = sum of two middle bricks
Middle brick = sum of two bottom bricks

Theorems

Basic Arithmetic Theorem
Linear Equations

Suitable Grade Level

Grades 5-7