Question:
Macy, sydmey, and Allie are sisters. macy is two years older than Sydney and Allie is one year less than half the age of sydney. if the sum of their ages is 31, how old is macy
Answer:
Macy is 14 years old
Solution:
Let the age of sydney be "S"
Given that,
macy is two years older than Sydney
Age of macy = S + 2
Allie is one year less than half the age of sydney
[tex]\text {Age of allie }= \frac{S}{2} - 1[/tex]
The sum of their ages is 31
Therefore,
[tex]S + S + 2 + \frac{S}{2} - 1 = 31\\\\2S + \frac{S}{2} = 31 - 1\\\\4S + S = 30 \times 2\\\\5S = 60\\\\\S = 12[/tex]
how old is Macy?
Age of macy = S + 2 = 12 + 2 = 14
Thus macy is 14 years old
