Subjects algebra

Percentage Decrease 39877B

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1. **State the problem:** We are given that a number $N$ decreased by 12% equals 132. We need to find the original number $N$. 2. **Write the expression for 12% decrease:** A 12% decrease means subtracting 12% of $N$ from $N$ itself. This can be written as: $$N - \frac{12N}{100}$$ 3. **Set up the equation:** According to the problem, this decreased value equals 132, so: $$N - \frac{12N}{100} = 132$$ 4. **Simplify the left-hand side:** Combine the terms by expressing both with a common denominator: $$\frac{100N}{100} - \frac{12N}{100} = \frac{88N}{100}$$ So the equation becomes: $$\frac{88}{100} \times N = 132$$ 5. **Solve for $N$:** Multiply both sides by the reciprocal of $\frac{88}{100}$: $$N = 132 \times \frac{100}{88}$$ 6. **Calculate the value:** Simplify the fraction $\frac{100}{88} = \frac{25}{22}$, so: $$N = 132 \times \frac{25}{22} = 6 \times 25 = 150$$ **Final answer:** $$\boxed{150}$$