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
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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.