a woman is four times older than her daughter five years ago the product of their age was 175 find their present age

w = 4 d

(w - 5)(d - 5) = 175

(4 d - 5)(d - 5) = 175 ... 4 d^2 - 25 d - 150 = 0

use quadratic formula to find d
... then substitute back to find w

yes. I Got the answer. 10 and 40.

Thankyou.
Sir,any short cuts for solving this pblm.

Let's assume the daughter's present age is 'x' years.

According to the given information, the woman's present age would then be 4x years.

Five years ago, the daughter was 'x - 5' years old, and the woman was '4x - 5' years old.

The product of their ages was 175 at that time:
(x - 5) * (4x - 5) = 175

Expanding the equation, we have:
4x^2 - 5x - 20x + 25 = 175
4x^2 - 25x + 25 - 175 = 0
4x^2 - 25x - 150 = 0

To solve this quadratic equation, we can use factoring. The equation can be factored as:
(4x + 15)(x - 10) = 0

Setting each factor to zero and solving for 'x', we have:

4x + 15 = 0 or x - 10 = 0

When 4x + 15 = 0, we get:
4x = -15
x = -15/4

However, since we're dealing with ages, we can disregard negative values. So, 'x' cannot be negative.

When x - 10 = 0, we get:
x = 10

Therefore, the daughter's present age is 10 years, and the woman's present age is 4 times that, which is 40 years.

To find their present age, let's assign variables to represent their ages.

Let's say the daughter's present age is "D" and the woman's present age is "W".

According to the given information, the woman is four times older than her daughter five years ago. We can express this as an equation:

W - 5 = 4(D - 5)

Next, we are given that the product of their ages five years ago was 175. So, we can also express this as an equation:

(W - 5) * (D - 5) = 175

Now we have a system of two equations. We can solve these equations simultaneously to find the values of D and W.

First, we can simplify the equation W - 5 = 4(D - 5):

W - 5 = 4D - 20

We can simplify this further by moving the terms around:

W - 4D = -20 + 5

W - 4D = -15

Next, we can substitute this expression for W in the second equation:

(W - 5) * (D - 5) = 175

(-15) * (D - 5) = 175

Now, we can solve for D:

-15(D - 5) = 175

Expand the left side:

-15D + 75 = 175

Subtract 75 from both sides:

-15D = 100

Divide both sides by -15:

D = -100 / -15

D = 6.67

Since we cannot have a fraction as an age, we round D to the closest whole number, which is 7.

Now that we have the daughter's age (D = 7), we can substitute it back into the first equation to find the woman's age (W):

W - 5 = 4(D - 5)

W - 5 = 4(7 - 5)

W - 5 = 4(2)

W - 5 = 8

Add 5 to both sides:

W = 8 + 5

W = 13

Therefore, the daughter's present age is 7, and the woman's present age is 13.