Subjects algebra

Pyramid Expression

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Pyramid Expression


1. **State the problem:** We have a pyramid of bricks where the top brick expression equals the sum of the two bricks below it. The expressions are: - Top brick: $8f + 7w + 13$ - Bottom left brick: $3f + 4w + 6$ - Bottom right brick: $?$ (unknown, to find) 2. **Set up the equation:** Since the top brick is the sum of the two bottom bricks, we have: $$8f + 7w + 13 = (3f + 4w + 6) + ?$$ 3. **Isolate the unknown expression:** Subtract the left bottom brick from the top brick: $$? = (8f + 7w + 13) - (3f + 4w + 6)$$ 4. **Simplify the right side:** $$? = 8f - 3f + 7w - 4w + 13 - 6$$ $$? = 5f + 3w + 7$$ 5. **Final answer:** The expression that should replace the question mark is: $$5f + 3w + 7$$