SOLUTION: a woman is older dan her daughter by 15 yrs, 10 yrs ago the ratio of their age was 4,1 find thier present age

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Question 1119161: a woman is older dan her daughter by 15 yrs, 10 yrs ago the ratio of their age was 4,1 find thier present age
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
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Who is dan? Woman is older than dan or what?

system%28w=d%2B15%2C%28w-10%29%2F%28d-10%29=4%29
-
%28d%2B15-10%29%2F%28d-10%29=4
%28d%2B5%29%2F%28d-10%29=4
d%2B5=4d-40
45=3d
d=15
.
.

Answer by ikleyn(52790) About Me  (Show Source):
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.
W = D + 15,        (1)

%28W-10%29%2F%28D-10%29 = 4.        (2)


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W - 10 = 4*D - 40

(D + 15) - 10 = 4*D - 40

D + 5 = 4*D - 40

5 + 40 = 4*D - D

45 = 3*D  ====>  D = 45%2F3 = 15.


Answer.  The daughter is 15 years old.  The women is (15+15) = 30 years old.


Answer by greenestamps(13200) About Me  (Show Source):
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If the woman is 15 years older than her daughter, then when the ratio of their ages was 4:1 their ages had to be 20 and 5. That was 10 years ago; so now the mother is 30 and the daughter is 15.

There was a bit of mental arithmetic there....

If the ratio of two numbers is 4:1, then the two numbers can be represented by 4x and x; the difference between the two numbers is then 4x-x = 3x. Since the difference in ages is 15, 3x=15 so x=5. Then the ages (10 years ago) were x=5 and 4x=20; the current ages are 5+10=15 and 20+10=30.