A cement block balances evenly on the scales with 3 quarters of a pound and 3…

Concept: When a balance (or any statement) says an unknown whole quantity equals a fixed amount plus a fraction of that same whole, translate it directly into a linear equation — let x be the whole, write the equation exactly as stated, then move every x-term to one side to isolate x.

1. Let the weight of the whole block be x pounds.

2. The scale balances one whole block against 3/4 pound plus 3/4 of a block, so x = 3/4 + (3/4)x.

3. Move the block term to the left side: x − (3/4)x = 3/4.

4. Combine like terms on the left: (1/4)x = 3/4.

5. Multiply both sides by 4 to isolate x: x = 3.

Cross-check: substituting x = 3 back into the right side gives 3/4 + (3/4)(3) = 3/4 + 9/4 = 12/4 = 3, which equals the left side — the scale balances exactly when the block weighs 3 pounds.