Yuki's age is four years more than one-fourth of Xena's age. Xena's age is 21 years and 6 months more than seven-eighths of Yuki's age. How old are Xena and Yuki?

y = .25x + 4

x = 7/8y +21.5

Substitute .25x+4 for y in second equation and solve for x. Insert that value into the first equation and solve for y. Check by inserting both values into the second equation.

To find the ages of Xena and Yuki, let's break down the given information step by step:

1. Let's assume Yuki's age as y and Xena's age as x.

2. According to the first statement, Yuki's age is four years more than one-fourth of Xena's age. Mathematically, this can be expressed as: y = (1/4)x + 4.

3. The second statement says that Xena's age is 21 years and 6 months more than seven-eighths of Yuki's age. Mathematically, this can be expressed as: x = (7/8)y + 21.5.

Now, we have a system of two equations:

y = (1/4)x + 4 ---(Equation 1)
x = (7/8)y + 21.5 ---(Equation 2)

To solve this system of equations, we can use the substitution method. Let's substitute Equation 1 into Equation 2:

x = (7/8)y + 21.5
x = (7/8)((1/4)x + 4) + 21.5
x = (7/32)x + 7/2 + 21.5
x - (7/32)x = 7/2 + 21.5
(25/32)x = 28/2 + 43/2
(25/32)x = 71/2
x = (71/2) * (32/25)
x ≈ 45.44

Therefore, Xena's age is approximately 45.44 years old.

Now, let's substitute this value of x back into Equation 1 to find Yuki's age:

y = (1/4)(45.44) + 4
y = 11.36 + 4
y ≈ 15.36

Therefore, Yuki's age is approximately 15.36 years old.

So, Xena is approximately 45.44 years old, and Yuki is approximately 15.36 years old.