Question 1119831: Dear Teacher,
I am so sorry to bother, but I really need some help with my assignment. This is the question:
Jenny has a younger sister Rose. Five years ago, Jenny was 10 times as old as Rose. Three years from now, Jenny will be twice as old as Rose.
a) What are Jenny and Rose's present age?
b) How old was Jenny when Rose was born?
Thank you so much!
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Jenny has a younger sister Rose.
j = Jenny's present age; r = Rose's
:
Write an equation for each statement, simplify
Five years ago, Jenny was 10 times as old as Rose.
j - 5 = 10(r-5)
j - 5 = 10r - 50
j = 10r - 50 + 5
j = 10r - 45
:
Three years from now, Jenny will be twice as old as Rose.
j + 3 = 2(r + 3)
j + 3 = 2r + 6
j = 2r + 6 -3
j = 2r + 3
:
j = j therfore
10r - 45 = 2r + 3
10r - 2r = 3 + 45
8r = 48
r = 48/8
r = 6 yrs is Roses age
Find j
j = 2(6) + 3
j = 12 + 3
j = 15 is Jenneys age
:
a) What are Jenny and Rose's present age? Obviously 15 and 6
:
b) How old was Jenny when Rose was born?
Subtract Rose's age from Jenny's
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
A solution using formal algebra, like the one provided by the other tutor, is of course a good exercise.
But if the question is on a competitive exam where speed is important, the problem can be solved far more quickly with a little logical analysis and some easy mental arithmetic.
(1) If Jenny was 10 times as old as Rose 5 years ago, then their ages then must have been 10 and 1, or 20 and 2, or 30 and 3, or ....
(2) Then their ages now must be 15 and 6, or 25 and 7, or 35 and 8, or ....
(3) Then their ages 3 years from now must be 18 and 9, or 28 and 10, or 38 and 11, or ....
Of course, you can stop with that first pair, because it satisfies the required condition that in 3 years Jenny will be twice as old as Rose.
And of course to answer the second question you simply find the difference in their ages -- either 5 years ago, or now, or 3 years from now.
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