MECHANICAL ENGINEERING LICENSE EXAM REVIEWER - Math Worded Age Problems - how old is the girl

MECHANICAL ENGINEERING LICENSE EXAM REVIEWER - Math Worded Age Problems - how old is the girl

PROBLEM

A girl, is one-third as old as her brother and 8 years younger than her sister. The sum of their ages is 38 years. How old is the girl?

Given
girl is 1/3 as old as brother

girl is also 8 years younger than sister

38 sum of their ages

Unknown
how old is the girl

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SOLUTION

Let
g = age of girl now

b = age of the girl's brother now

s = age of the girl's sister now

equation 1
girl is 1/3 as old as brother

g = b/3

b = 3g

equation 2
girl is 8 years younger than sister

g = s - 8

s = g + 8

equation 3

38 sum of their ages

b + s + g = 38

substituting the values of b and s from equations 1 and 2 respectively, into equation 3

b + s + g = 38

but
b = 3g
s = g + 8

3g + (g + 8) + g = 38
3g + g + 8 + g = 38
5g = 38 - 8
5g = 30
g = 30/5
g = 6
(age of girl)

age of girl's brother
b = 3g
b = 3 x 6
b = 18

age of girl's sister
s = g + 8
s = 6 + 8
s = 14

checking:

sum of their ages 38
6 + 18 + 14 = 38
38 = 38

girl is 1/3 as old as brother
6 = 1/3 of 18
6 = 18/3

girl is 8 years younger than sister
14 - 6 = 8

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