Question 1182898: 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 3 solutions by josgarithmetic, greenestamps, math_tutor2020:
Answer by josgarithmetic(39617)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
The other tutors have great answers.
My method may not be as efficient, but it's another pathway at least.
Four years ago, the ratio of Kim's age to her daughter's age was 3:1
Meaning that the mother was triple in age compared to the daughter
(eg: mother = 30 and daughter = 10)
x = daughter's age four years ago
3x = Kim's age four years ago
Let's fast-forward the calendar four years into the future.
This is so we arrive at the present day ages
x+4 = daughter's age now
3x+4 = mother's age now
The ratio of these present day ages, mother to daughter, is 5:2
So,
mothersAge/daughtersAge = 5/2
(3x+4)/(x+4) = 5/2
2(3x+4) = 5(x+4)
6x+8 = 5x+20
6x-5x = 20-8
x = 12
The daughter was 12 years old 4 years ago.
Therefore, she must be 12+4 = 16 years of age currently.
The mother was 3x = 3*12 = 36 years old 4 years ago.
She is now 36+4 = 40 years old.
As a check,
mothersAge/daughtersAge = 40/16 = (8*5)/(8*2) = 5/2, which lets us know we did things correctly.
The last thing to do is add 6 years onto Kim's current age to find how old she will be 6 years into the future.
40+6 = 46
Answer: 46 years old
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