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6.  The present age of a mother is 3 years more than three times the age of her daughter. Three years hence, the mother’s age will be 10 years more than twice the age of the daughter. Find the present age of the mother.40 years32 years33 years25 years

Question

6.  The present age of a mother is 3 years more than three times the age of her daughter. Three years hence, the mother’s age will be 10 years more than twice the age of the daughter. Find the present age of the mother.40 years32 years33 years25 years

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Solution

Let's denote the present age of the mother as M and the present age of the daughter as D.

From the problem, we have two equations:

  1. M = 3D + 3 (The present age of a mother is 3 years more than three times the age of her daughter)

  2. M + 3 = 2(D + 3) + 10 (Three years hence, the mother’s age will be 10 years more than twice the age of the daughter)

We can simplify the second equation to: M = 2D + 6 + 10 - 3 = 2D + 13

Now we have two equations with the same left side (M), so we can set the right sides equal to each other:

3D + 3 = 2D + 13

Solving this equation for D gives: D = 10

Substituting D = 10 into the first equation gives: M = 3*10 + 3 = 33

So, the present age of the mother is 33 years.

This problem has been solved

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