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?
To solve this problem, let's assign variables to the ages of both Xena and Yuki.
Let's say X is Xena's age, and Y is Yuki's age.
According to the information given:
1) Yuki's age is four years more than one-fourth of Xena's age.
This can be written as: Y = (1/4)X + 4
2) Xena's age is 21 years and 6 months more than seven-eighths of Yuki's age.
This can be written as: X = (7/8)Y + 21.5
Now we have a system of two equations. To solve for X and Y, we can substitute the value of Y from the first equation into the second equation.
Substituting (1/4)X + 4 for Y in the second equation, we get:
X = (7/8)((1/4)X + 4) + 21.5
Let's solve for X:
Expand the equation:
X = (7/8)(1/4)X + (7/8)(4) + 21.5
Combine like terms:
X = (7/32)X + 7/2 + 21.5
Simplify:
X - (7/32)X = 7/2 + 21.5
Multiply both sides by 32 to eliminate the fraction:
32X - 7X = 112 + 688
Combine like terms:
25X = 800
Divide both sides by 25:
X = 32
Now we have found Xena's age, which is 32 years.
To find Yuki's age, we can substitute this value back into the first equation:
Y = (1/4)(32) + 4
Y = 8 + 4
Y = 12
Therefore, Xena is 32 years old and Yuki is 12 years old.