A Boy Is 10 Years Older Than His Brother In 4 Years

A Boy Is 10 Years Older Than His Brother In 4 Years He Will Be Twi

A boy is 10 years older than his brother. In 4 years he will be twice as old as his brother. Find the present age of each.

Paper For Above instruction

Understanding age-related word problems requires constructing algebraic equations based on the constraints provided. In this problem, we are told that a boy is 10 years older than his brother, and in four years, he will be twice as old as his brother. To solve this, let us define variables for their current ages:

Let B = current age of the boy, and Br = current age of the brother. Based on the problem statement, we can set up the following equations:

  • Age difference: B = Br + 10
  • Future ages in 4 years: B + 4 = 2(Br + 4)

From the second equation, expand and simplify:

B + 4 = 2Br + 8

Rearranged to isolate B:

B = 2Br + 4

Now, substitute this into the age difference equation:

2Br + 4 = Br + 10

Simplify:

2Br - Br = 10 - 4

Br = 6

Having found Br = 6 (brother's current age), find B (boy's current age):

B = Br + 10 = 6 + 10 = 16

Therefore, the boy is currently 16 years old, and his brother is 6 years old.

This problem exemplifies how algebraic representations of word problems enable precise solutions. It demonstrates the importance of defining variables clearly and forming equations based on given relationships and conditions. The method can be generalized to a wide range of age-related problems with similar structures, emphasizing the importance of translating written descriptions into algebraic expressions for effective problem-solving.

References

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