Create a captivating image of a Caucasian woman and her daughter who are at different stages of life. The woman is in her middle age, she has brown hair and is elegantly dressed. She is holding a mathematics book in her hands. Her daughter, a young girl, possibly in her teenage years is of a playful spirit. She is seated next to her mother and playing with an abacus. In the background, you can see a ticking wall clock and a calendar, indicating the passage of time. Remember, there should be no text in the image.

The sum of the ages of a woman and her daughter is 46years.In 4 years, the ratio of their ages will be 7:2. Find their present ages.

Let the woman's age=x

Let the daughter's age=y
Therefore
(x+y)=46
Make x the subject of theach above equation.
; x=46-y (equation 1)
4 years ago;
The woman=x+4
the daughter =y+4

The ratio is
7:2=(x+4):(y+4)
Cross multiply
7(y+4)=2 (x+4)
7y+28=2x+8 (equation 2)

Substitute (equation 1) into ( equation 2)

7y+28=2(46-y)+8
7y+28=92 -2y+8
Group like terms
7y+2y=92+8-28
9y=72
Divide all sides by 9

Y=8.

Substitute y=8 into (equation 1)
°: x=46-y
x=46-8
X=38.

Therefore
Woman's age =38
Daugher's age=8

In four years, the total of the ages will be 46+4+4=54 years.

The ratio in four years will be 7:2
So
age of daughter in four years
= 54*(2/(7+2))=12
age of mother in four years
= 54*(7/(7+2))=42

Continue to find their present ages.

Very comprehensive, but easy to understand

Great, well explanation

Thank you! I'm glad you found it helpful. If you have any other questions, feel free to ask.

To solve this problem, we can set up a system of equations based on the given information.

Let's assume the present age of the woman is W years and the present age of her daughter is D years.

According to the problem, the sum of their ages is 46 years:
W + D = 46 Equation 1

In 4 years, the ratio of their ages will be 7:2. So, we can set up another equation using this information:
(W+4) / (D+4) = 7/2 Equation 2

To solve this system of equations, we can use the method of substitution or elimination.

Let's solve it using the substitution method:

From Equation 1, we have: W = 46 - D

Now, substitute this value of W in Equation 2:

(46 - D + 4) / (D + 4) = 7/2

Simplifying the left side:

(50 - D) / (D + 4) = 7/2

Cross-multiply:

2(50 - D) = 7(D + 4)

Simplify:

100 - 2D = 7D + 28

Combine like terms:

100 - 28 = 7D + 2D

72 = 9D

Divide both sides by 9:

D = 8

Substitute this value of D back into Equation 1 to find W:

W + 8 = 46

W = 46 - 8

W = 38

Therefore, the present age of the woman is 38 years and the present age of her daughter is 8 years.

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