Math Problem Statement
Solution
The problem is asking to find the value of 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: , , and
According to the rule of the pyramid:
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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 and , so it equals .
- The right middle brick is the sum of and , so it equals .
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The top brick is the sum of the two middle bricks: Simplifying: Solving for :
Thus, the value of is .
Would you like any more details or explanations on this solution?
Here are 5 related questions you can explore:
- What would the bottom numbers be if ?
- How do number pyramids help in understanding algebraic relationships?
- Can you build a larger number pyramid with a similar rule and solve it?
- How does the concept of solving simultaneous equations relate to this problem?
- 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