Answer:
The younger brother is 7 years old and the older brother is 10 years old.
Explanation:
1. Let x represent the age of the younger brother and y represent the age of the older brother.
Then, if they are three years apart in age, the age of the older brother is given by the age of the younger brother plus 3:
y = x + 3
2. If the sum of their ages is 17, then:
x + y = 17
3. There are many different ways to solve the question from this point onwards, however I will show how we may substitute the first equation into the second as it doesn't require any rearranging of formulas.
Thus, if y = x + 3, then:
x + y = x + (x + 3)
If x + y = 17, then:
x + x + 3 = 17
2x + 3 = 17
2x = 14 (Subtract 3 from each side)
x = 7 (Divide both sides by 2)
Since x represents the age of the younger brother, we now know that he is 7 years old.
4. To find the older brother's age, we simply substitute x = 7 into the first equation:
y = x + 3
y = 7 + 3
y = 10
Therefor, the older brother is 10 years old.