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.
If you setup algebra equations for this problem, you can solve for the equations and get their ages.
Do you know what the algebra would look like?
w+d = 46
(w+4)/(d+4) = 7/2
Now just solve for w and d.
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 given information, the sum of their ages is 46, so we have the equation:
w + d = 46 (Equation 1)
In 4 years, the woman will be w+4 years old, and the daughter will be d+4 years old. The ratio of their ages at that time will be 7:2, so we have the equation:
(w+4)/(d+4) = 7/2 (Equation 2)
To solve these equations, we can rearrange Equation 1 to solve for w:
w = 46 - d
Substitute this value of w into Equation 2:
(46 - d + 4) / (d + 4) = 7/2
Let's cross-multiply:
2(46 - d + 4) = 7(d + 4)
Simplify:
92 - 2d + 8 = 7d + 28
Combine like terms:
-2d + 100 = 7d + 28
Move the variables to one side:
-9d = -72
Divide both sides by -9:
d = 8
Substitute this value of d back into Equation 1:
w + 8 = 46
Subtract 8 from both sides:
w = 38
Therefore, the woman's present age is 38 years and her daughter's present age is 8 years.
To solve this problem, let's assign variables to the unknowns. Let the woman's age be represented by "x" and the daughter's age be represented by "y".
From the given information, we can create two equations:
1. The sum of their ages is 46: x + y = 46
2. In 4 years, the ratio of their ages will be 7:2: (x + 4) : (y + 4) = 7 : 2
We can solve this system of equations to find the values of x and y.
First, let's rearrange the second equation to eliminate the fractions:
2(x + 4) = 7(y + 4)
Now, simplify and expand:
2x + 8 = 7y + 28
Rearrange this equation:
2x - 7y = 20 (equation 3)
Now, let's solve equations 1 and 3 simultaneously using the method of substitution.
From equation 1, we have: x = 46 - y
Substituting this value of x into equation 3, we get:
2(46 - y) - 7y = 20
92 - 2y - 7y = 20
92 - 9y = 20
-9y = 20 - 92
-9y = -72
y = (-72)/(-9)
y = 8
Now, substitute the value of y back into equation 1 to find x:
x + 8 = 46
x = 46 - 8
x = 38
So, the woman's present age is 38 years, and the daughter's present age is 8 years.