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What value of b makes this multiplication sentence true?

Hint: Use properties of multiplication.

(1 + b) · 578.2 = 578.2 + 230.51 · 578.2

b

1 answer

To solve the equation \( (1 + b) \cdot 578.2 = 578.2 + 230.51 \cdot 578.2 \), we can start by factoring out \( 578.2 \) on the right-hand side:

  1. Rewrite the right-hand side: \[ 578.2 + 230.51 \cdot 578.2 = 578.2 \cdot (1 + 230.51) \]

  2. This simplifies the equation to: \[ (1 + b) \cdot 578.2 = 578.2 \cdot (1 + 230.51) \]

  3. We can then divide both sides of the equation by \( 578.2 \) (assuming \( 578.2 \neq 0 \)): \[ 1 + b = 1 + 230.51 \]

  4. Subtract \( 1 \) from both sides: \[ b = 230.51 \]

Thus, the value of \( b \) that makes the multiplication sentence true is: \[ \boxed{230.51} \]