Question 635990: my current age is 4 times what my sisters age was 20 years ago. i am now twice as old as i was 20 years ago. ten years ago, my sisters age was 1/2 of my current age. ten years ago, my age was 1.5 times my sisters age. what are our current ages?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Let y = your current age
Let s = sister's current age
:
Write an equation for each statement, simplify as much as possible:
:
"my current age is 4 times what my sisters age was 20 years ago."
y = 4(s-20)
y = 4s - 80
:
" I am now twice as old as i was 20 years ago."
y = 2(y-20)
y = 2y - 40
40 = 2y -y
y = 40 yr, your present age
:
Right here you know enough to solve this
40 = 4s - 80
40 + 80 = 4s
s = 120/4
s = 30 is the sisters age
:
You can check this using the rest of the equations with y=40, s=30
:
ten years ago, my sisters age was 1/2 of my current age. "
s - 10 = .5y
multiply both sides by 2
2(s-10) = y
2s - 20 = y
:
"ten years ago, my age was 1.5 times my sisters age."
y - 10 = 1.5(s-10)
y - 10 = 1.5s - 15
y = 1.5s - 15 + 10
y = 1.5s - 5
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Two unknowns, two equations are sufficient.
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