SOLUTION: A woman is older than her daughter by 25 years. Three years ago, the ratio of their ages was 3:1. Find their present ages.

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Question 1190483: A woman is older than her daughter by 25 years. Three years ago, the ratio of their ages was 3:1. Find their present ages.
Found 2 solutions by VFBundy, greenestamps:
Answer by VFBundy(438)   (Show Source): You can put this solution on YOUR website!
Woman's age = W
Daughter's age = D

Make two equations:

W = D + 25
W - 3 = 3(D - 3)

Simplify the second equation:

W = D + 25
W - 3 = 3D - 9

Move the variables to left side and the constants to right side:

W - D = 25
W - 3D = -6

Multiply the first equation by -3:

-3W + 3D = -75
W - 3D = -6

Add the equations together:

-2W = -81

Solve for W:

W = 40.5

Substitute W = 40.5 into either of the original equations:

W = D + 25

40.5 = D + 25

Solve for D:

D = 15.5

Woman's age = W = 40.5
Daughter's age = D = 15.5

Check it:

"A woman is older than her daughter by 25 years."

40.5 is 25 years older than 15.5.

"Three years ago, the ratio of their ages was 3:1."

Three years ago, the woman was 37.5 and the daughter was 12.5. The ratio of 37.5 to 12.5 is 3:1.

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


Using two variables to solve the equation makes for a lot more work than using only one....

x = daughter's age now
x+25 = woman's age now

x-3 = daughter's age 3 years ago
x+22 = woman's age 3 years ago

3 years ago the woman was 3 times as old as her daughter:

x+22=3(x-3)
x+22=3x-9
31=2x
x=15.5

The problem is not valid; in problems involving ages, the ages must be whole numbers.


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