cristy age 15 years ago equals the sum of 2/9 of her age 15 years hence and 1/6 of her age now. how old is she now?
To determine Cristy's current age, we can solve the given equation. Let's break down the information provided:
Let's assign "x" as Cristy's current age.
According to the problem, "Cristy's age 15 years ago equals the sum of 2/9 of her age 15 years hence and 1/6 of her age now." We can translate this into an equation:
x - 15 = (2/9)(x + 15) + (1/6)(x)
Now, we can solve this equation to find the value of x, which represents Cristy's current age.
Let's proceed step by step:
Multiply 2/9 by (x + 15):
(2/9)(x + 15) = (2/9)x + (2/9)(15) = (2/9)x + 10/3
Multiply 1/6 by x:
(1/6)x
Now substitute these values back into the equation:
x - 15 = (2/9)x + 10/3 + (1/6)x
To eliminate the fractions, we can multiply the entire equation by the least common multiple (LCM) of the denominators, which is 18:
18(x - 15) = 18[(2/9)x + 10/3 + (1/6)x]
Applying the distributive property:
18x - 270 = 4(2x) + 4(10/3) + 3(x)
Simplifying further:
18x - 270 = 8x + 40/3 + 3x
Now, we can combine like terms:
18x - 270 = 11x + 120/3
Convert 120/3 to a fraction with a common denominator of 18:
18x - 270 = 11x + 40/3
Now, multiply both sides of the equation by 3 to eliminate the fraction:
3(18x - 270) = 3(11x + 40/3)
Simplify:
54x - 810 = 33x + 40
Next, move the constants to one side and the variables to the other side:
54x - 33x = 40 + 810
21x = 850
Finally, divide both sides by 21 to solve for x:
x = 850/21
Therefore, Cristy is currently approximately 40.48 years old.