A woman is now 4 times older than her daughter.Six years ago,the product of their ages was 136.Find their present ages.
You can solve this easily as follows:
Let the woman age now = x
Daughter age now = y
First information says that
x = 4y
second information says that
(x-6)(y-6) =136
substitute from first into second
(4y-6)(y-6) = 136
4 y^2 - 30 y + 36 = 136
4 y^2 - 30y - 100 = 0
Simplfying
2 y^2 - 15y -50 =0
(2y+5)(y-10)=0
y = 10 as age can not be negative
Woman age = 4 * 10 = 40 years
Daughter age = 10 years
Good luck
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correct
Well, well, well, it seems like we have a classic age-related puzzle here. Let's get cracking, shall we?
Let's call the daughter's current age "D" and the woman's current age "W". According to the information given, we know that W = 4D.
Six years ago, the daughter's age would have been D - 6, and the woman's age would have been W - 6.
Now, we also know that six years ago, the product of their ages was 136. So we have the equation (D - 6) * (W - 6) = 136.
Substituting W = 4D into the equation, we have (D - 6) * (4D - 6) = 136.
Expanding this equation, we get 4D^2 - 30D + 36 = 136.
Rearranging things a bit, we have 4D^2 - 30D - 100 = 0.
Now, it's time to solve for D. Using my handy-dandy humor equation solver, I find that D = 7.5 or -3.
Well, obviously we can't have a negative age, so the daughter's current age must be 7.5... Wait, what?!
Sorry, folks, but it seems like this puzzle might need some tweaks. I think we better head back to the drawing board on this one!
To find the present ages of the woman and her daughter, let's follow these steps:
1. Set up variables: Let's assume the daughter's present age is "x" and the woman's present age is "4x".
2. Express the relationship between their ages: The problem states that the woman is now 4 times older than her daughter, so we can write the equation: 4x = x + 4
3. Solve the equation: Simplify the equation by subtracting x from both sides: 3x = 4. Then divide both sides by 3: x = 4/3.
This tells us that the daughter's present age is 4/3.
Now, we need to find the woman's present age using the value of x we have found.
4. Substitute the value of x into the equation: The daughter's present age (x) is 4/3, and the woman's age is 4 times that. So the woman's present age is 4 * (4/3) = 16/3.
Therefore, the daughter's present age is 4/3, and the woman's present age is 16/3.