Question 1191852: Michael and Janet are 10 years apart in age. In 24 months Michael will be twice as old as Janet. How old is Janet now?
Found 3 solutions by josgarithmetic, ikleyn, math_tutor2020:
Answer by josgarithmetic(39617)   (Show Source):
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
From the post, it is clear that in 2 years M will be twice as old as J and 10 years older than J.
Hence, in 2 years M will be 20 years old, while J will be 10 years old.
Hence, today M is 20-2 = 18 years old, while J is 10-2 = 8 years old. ANSWER
Solved MENTALLY.
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
j = Janet's age currently
j+10 = Michael's age currently
Whatever number j is, add 10 to get Michael's age.
The two are always separated by a gap of 10 years.
12 months = 1 year
2*12 months = 2*1 year
24 months = 2 years
In 2 years time, we have these future ages
Janet = j+2
Michael = (j+10)+2 = j+12
At this future point in time, Michael is twice as old as Janet
Michael's future age = 2*(Janet's future age)
j+12 = 2*(j+2)
j+12 = 2j+4
12-4 = 2j-j
8 = j
j = 8
Janet is currently 8 years old
Michael is currently j+10 = 8+10 = 18 years old.
In 2 years, we have these future ages
Janet = 8+2 = 10
Michael = 18+2 = 20
we see that Michael is indeed twice as old as Janet at this point (20 = 10*2).
The answer has been confirmed.
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Here's another approach:
j = Janet's age 2 years into the future
j+10 = Michael's age 2 years into the future
Michael's future age = 2*(Janet's future age)
j+10 = 2*(j)
j+10 = 2j
10 = 2j-j
10 = j
j = 10
This says Janet will be 10 years old when we fast forward two years into the future.
Rewinding two years back, to get to the present day, gets us to 10-2 = 8 as the final answer.
This method effectively follows the same idea as the previous section.
Except this time, the frame of reference starts off based in the future at first before rewinding back.
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Answer: 8 years old
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