The respective ratio of the present age of a mother and daughter is 7 : 1. Four years ago the respective ratio of their age was 19 : 1. What will be the mother’s age four years from now ?
Question
The respective ratio of the present age of a mother and daughter is 7 : 1. Four years ago the respective ratio of their age was 19 : 1. What will be the mother’s age four years from now ?
Solution
Sure, let's solve this step by step:
Step 1: Let's assume the present age of the mother is 7x and the present age of the daughter is x.
Step 2: According to the problem, four years ago the ratio of their ages was 19:1. So, we can write this as (7x - 4) / (x - 4) = 19/1.
Step 3: Simplifying this equation, we get 7x - 4 = 19x - 76.
Step 4: Rearranging the terms, we get 19x - 7x = 76 + 4.
Step 5: This simplifies to 12x = 80.
Step 6: Solving for x, we get x = 80 / 12 = 6.67 years. This is the present age of the daughter.
Step 7: Substituting x = 6.67 in the equation 7x = mother's age, we get the mother's present age as 7 * 6.67 = 46.69 years.
Step 8: The question asks for the mother's age four years from now. So, we add 4 to the mother's present age to get 46.69 + 4 = 50.69 years.
So, the mother's age four years from now will be approximately 51 years (if we round to the nearest whole number).
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