SOLUTION: A sister has 3 younger brothers whose ages are equally spaced. At present the sister's age is equal to the sum of her brothers' ages. Five years ago the sum of the brothers' ages w

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Question 521120: A sister has 3 younger brothers whose ages are equally spaced. At present the sister's age is equal to the sum of her brothers' ages. Five years ago the sum of the brothers' ages was half the sister's present age and the eldest brother was 4 times as old as the youngest. What are the present ages of the sister and her 3 brothers?
I'm using system of equations and I managed to come up with 3 of the equations. I realize I need a 4th one because I have 4 unknown variables. I need help immediately.
Answer by Maths68(1474) About Me  (Show Source):
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Let
Present age of Sister = s
Present age of Eldest brother = a
Present age of younger brother = b
Present age of youngest brother = c


At present the sister's age is equal to the sum of her brothers' ages.
s=a+b+c...................(1)

Five years ago
age of Eldest brother was = a-5
age of younger brother was = b-5
age of youngest brother was = c-5
Then
the sum of the brothers' ages was half the sister's present age
s/2=a-5+b-5+c-5
s/2=a+b+c-15
s =2(a+b+c-15).........(2)
Put the value of a+b+c from (1) to (2)
s = 2(s-15)
s=2s-30
s=30

And the eldest brother was 4 times as old as the youngest
a-5=4(c-5)
a-5=4c-20
a=4c-15.................(3)


Since their ages are equally spaced sum of ages of eldest brother and youngest brother divide by 2 will be equal to the age of younger brother
b=(a+c)/2
2b=a+c...................(4)

Put the value of 's' and (a+c) in equation (1)
s=a+b+c
s=(a+c)+b
30=2b+b
30=3b
30/3=3b/3
10=b
b=10

Now again put the value of 'b' and 's' in equation (1)
30=a+10+c
30-10=a+c
20=a+c
20-c=a
a=20-c...........(5)

Put the value of 'a' from (5) to (3)
20-c=4c-15
-c-4c=-15-20
-5c=-35
-5c/-5=-35/-5
c=7
Put the value of 'c' in (3)
a=4c-15
a=4(7)-15
a=28-15
a=13


Present age of Sister = s = 30 years old
Present age of Eldest brother = a = 13 years old
Present age of younger brother = b = 10 years old
Present age of youngest brother = c = 7 years old
Check
======

13+10+7= 30 (which is present age of sister)

5 years back
============
age of Eldest brother was = a-5 = 13-5= 8
age of younger brother was = b-5 = 10- 5 = 5
age of youngest brother was = c-5 = 7-5 = 2
8+5+2 = 15 (which is half of the present age of sister)
And the eldest brother was 4 times as old as the youngest
Eldest brother was 8 which is 4 times of 2.