SOLUTION: I am four times older than my sister was when she was half as young as I was. In 15 years our combined ages will be 100. How old are we now? Solution: Let x = your age

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Question 363118:
I am four times older than my sister was when she was half as young as I was. In 15 years our combined ages will be 100. How old are we now?
Solution:
Let x = your age
y = your sister's age
n = no. of years ago when your sister was half as young as you were
Equation 1:
x = 4(y-n)
Equation 2:
y-n = (x-n)/2
2y-2n = x-n
n = 2y-x
Equation 3:
x+15+y+15 = 100
x+y = 70
Substituting the n = 2y-x in Equation 1
x = 4(y-n)
= 4[y-(2y-x)]
= 4(y-2y+x)
= -4y + 4x
= 4y/3
Substituting x = 4y/3 in Equation 3
x+y = 70
4y/3+y= 70
3[4y/3+y = 70]
4y+3y = 210
7y = 210
y = 30 Your sister's age now is 30 yrs old
x = 4/3(30)
= 40 Your age now is 40 yrs old
Answer by amoresroy(361) About Me  (Show Source):
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Solution:
Let x = your age
y = your sister's age
n = no. of years ago when your sister was half as young as you were
Equation 1:
x = 4(y-n)
Equation 2:
y-n = (x-n)/2
2y-2n = x-n
n = 2y-x
Equation 3:
x+15+y+15 = 100
x+y = 70
Substituting the n = 2y-x in Equation 1
x = 4(y-n)
= 4[y-(2y-x)]
= 4(y-2y+x)
= -4y + 4x
= 4y/3
Substituting x = 4y/3 in Equation 3
x+y = 70
4y/3+y= 70
3[4y/3+y = 70]
4y+3y = 210
7y = 210
y = 30
Your sister's age now is 30 yrs old
x = 4/3(30)
= 40
Your age now is 40 yrs old