two years ago a woman was 4 times as old as her daughter. three years from now the mother will be only threw times as old as her daughter. How old are each of them now?
w-2 = 4(d-2)
w+3 = 3(d+3)
To solve this problem, we can set up a system of equations based on the information given.
Let's say the current age of the daughter is x, and the current age of the mother is y.
According to the first statement, "two years ago, a woman was 4 times as old as her daughter," we can set up the equation: (y-2) = 4(x-2).
According to the second statement, "three years from now, the mother will be only three times as old as her daughter," we can set up the equation: (y+3) = 3(x+3).
Now, we can solve this system of equations to find the values of x and y, representing the ages of the daughter and the mother, respectively.
Let's solve the first equation for y:
y - 2 = 4x - 8
y = 4x - 6
Substitute this value of y into the second equation:
4x - 6 + 3 = 3x + 9
4x - 3 = 3x + 9
4x - 3x = 9 + 3
x = 12
Now substitute the value of x back into the first equation to find y:
y = 4(12) - 6
y = 42
So, the current age of the daughter is x = 12, and the current age of the mother is y = 42.