a is two years older than b who is twice as old as c. if the total of the ages of a, b and c be 27, then how old is b?
Solution:
Let’s express the problem in terms of equations.
Given:
a = b + 2 (a is two years older than b)
b = 2c (b is twice as old as c)
a + b + c = 27 (the total of their ages is 27)
We can solve this system of equations to find the values of a, b, and c.
Substituting the value of b in terms of c into the first equation, we have:
a = 2c + 2
Now, substitute the values of a and b in the third equation:
(2c + 2) + (2c) + c = 27
5c + 2 = 27
5c = 27 - 2
5c = 25
c = 25/5
c = 5
Now that we have found the value of c, we can find the values of a and b.
a = 2c + 2
a = 2(5) + 2
a = 10 + 2
a = 12
b = 2c
b = 2(5)
b = 10
Therefore, b is 10 years old.
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