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(1-1/4)x(1-1/5)x(1-1/6)x(1-1/7)x(1-1/8)x(1-1/9)=a/75

2 min read Jun 16, 2024
(1-1/4)x(1-1/5)x(1-1/6)x(1-1/7)x(1-1/8)x(1-1/9)=a/75

Solving for "a" in the Equation: (1-1/4)x(1-1/5)x(1-1/6)x(1-1/7)x(1-1/8)x(1-1/9)=a/75

This problem involves simplifying a series of multiplications and then solving for an unknown variable. Let's break it down step by step:

Simplifying the Left-Hand Side

  1. Simplify each term:

    • (1 - 1/4) = 3/4
    • (1 - 1/5) = 4/5
    • (1 - 1/6) = 5/6
    • (1 - 1/7) = 6/7
    • (1 - 1/8) = 7/8
    • (1 - 1/9) = 8/9

  2. Multiply the simplified terms: (3/4) * (4/5) * (5/6) * (6/7) * (7/8) * (8/9) = (3 * 4 * 5 * 6 * 7 * 8) / (4 * 5 * 6 * 7 * 8 * 9)

  3. Cancel out common factors: This leaves us with 3/9 which simplifies to 1/3

Solving for "a"

Now we have the equation: 1/3 = a/75

To solve for "a", we can cross-multiply:

  1. Multiply the numerator of the first fraction by the denominator of the second fraction: 1 * 75 = 75

  2. Multiply the denominator of the first fraction by the numerator of the second fraction: 3 * a = 3a

  3. Set the results equal to each other: 75 = 3a

  4. Isolate "a" by dividing both sides by 3: 75 / 3 = a

Therefore, a = 25

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