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Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Question

Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360.

We would like to find Rohan’s present age.

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Solution

Sure, let's solve this step by step:

  1. Let's denote Rohan's present age as 'x'. Therefore, Rohan's mother's present age would be 'x + 26'.

  2. According to the problem, 3 years from now, the product of their ages will be 360. So, we can write this as an equation: (x + 3) * (x + 26 + 3) = 360.

  3. Simplifying the equation, we get: (x + 3) * (x + 29) = 360.

  4. Expanding this, we get: x^2 + 32x + 87 = 360.

  5. Subtract 360 from both sides to set the equation to zero: x^2 + 32x + 87 - 360 = 0.

  6. Simplify further to get: x^2 + 32x - 273 = 0.

  7. This is a quadratic equation in the form of ax^2 + bx + c = 0. We can solve this equation using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a).

  8. Substituting the values, we get: x = [-32 ± sqrt((32)^2 - 41(-273))] / (2*1).

  9. Simplifying further, we get: x = [-32 ± sqrt(1024 + 1092)] / 2.

  10. Simplifying further, we get: x = [-32 ± sqrt(2116)] / 2.

  11. Simplifying further, we get: x = [-32 ± 46] / 2.

  12. We get two solutions: x = 7 or x = -39.

  13. Since age cannot be negative, we discard -39. Therefore, Rohan's present age is 7 years.

This problem has been solved

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