SOLUTION: The ratio of Kim's age to her daughter's age is 5 : 2. Four years ago, the ratio of their ages was 3 : 1. How old will Kim be in 6 years' time?

Question 1202870: The ratio of Kim's age to her daughter's age is 5 : 2. Four years ago, the ratio of their ages was 3 : 1. How old will Kim be in 6 years' time?

Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
k = kim''s age
d = kim's dauaghter's age.
you get:
k/d = 5/2
(k-4)/(d-4) = 3/1
from k/d = 5/2, you get k = 5d/2
from (k-4)/(d-4) = 3/1, you get:
k = 3*(d-4) + 4 which becomes k = 3d-8.
this means that 5d/2 = 3d-8 because they are both equal to k.
multiply both sides of this equation by 2 to get 5d = 6d-16
solve for d to get d = 16
since k = 5d/2, you get k = 40
you now know that k = 40 and d = 16
k/d becomes 40/16 which is equal to 5/2.
(k-4)/(d-4) becomes 36/12 which is equal to 3/1.
all the ratios work out indicating the value of k and d are good.
since k = 40, then k + 6 = 46.
that's your answer.
kay will be 46 years old in 6 years.

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

When the given information in a problem includes a ratio, the amount of work needed to solve the problem is nearly always less if you use that ratio to set up the problem. In this problem, given the ratio 5:2 of their current ages....

Let 5x = Kim's age
Let 2x = daughter's age

Then

5x-4 = Kim's age 4 years ago
2x-4 = daughter's age 4 years ago

The ratio of their ages 4 years ago was 3:1.

Kim's age now is 5x = 40; 6 years from now it will be 46.

ANSWER: 46

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