SOLUTION: A brother is 3 years older than his sister, five years ago, the ratio of their ages were 4:3 find their present ages

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Question 1206003: A brother is 3 years older than his sister, five years ago, the ratio of their ages were 4:3 find their present ages
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52803) About Me  (Show Source):
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A brother is 3 years older than his sister, five years ago, the ratio of their ages highlight%28cross%28were%29%29 was 4:3.
Find their present ages
~~~~~~~~~~~~~~~~~~~~~~~ 

Let b be the brother's age 5 years ago.
Then the sister's age at that time was (b-3) years.


From the problem, we have this proportion

    b%2F%28b-3%29 = 4%2F3.


Cross multiply and find "b"

    3b = 4*(b-3)

    3b = 4b - 12

    12 = 4b - 3b

    12 =   b

     b = 12.


5 years ago the brother was 12 years old; the sister was 12-3 = 9 years old.

Hence, now the brother is 12+5 = 17 years old; the sister is 9+5 = 14 years old.    ANSWER

Solved.



Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Brother is 3 years older than his sister,...
x sister
x+3 brother


Five years ago
x-5 sister
x-2 brother
brother to sister ratio 4:3

%28x-2%29%2F%28x-5%29=4%2F3
4%28x-5%29=3%28x-2%29
4x-20=3x-6
highlight%28x=14%29

Brother, x%2B3=highlight%2817%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Given the ratio of their ages 5 years ago to be 4:3, one good way to start on the problem is like this:

Let 4x = brother's age 5 years ago
Let 3x = sister's age 5 years ago

The difference in their ages 5 years ago was 4x-3x = x; the difference in their ages (now and always) is 3 years. So

x=3; the brother's age 5 years ago was 4x=12; the sister's age 5 years ago was 3x=9; and...

ANSWER: The brother's age is 12+5 = 17; the sister's age is 9+5 = 14