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? Thank you.
y = 1/4x + 4
x = 7/8y + 21.5
Substitute 1/4x+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 solve this problem, we will use algebraic expressions to represent the ages of Xena and Yuki.
Let's start by assigning variables:
Let's say Xena's age is represented by 'X' and Yuki's age is represented by 'Y'.
According to the first statement, Yuki's age is four years more than one-fourth of Xena's age:
Y = (1/4)X + 4 ...........(equation 1)
According to the second statement, Xena's age is 21 years and 6 months more than seven-eighths of Yuki's age:
X = (7/8)Y + 21.5 ...........(equation 2)
We have two equations with two variables. We can solve this system of equations to find the values of X and Y.
To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method:
From equation 2, we can isolate Y:
Y = (8/7)(X - 21.5) ...........(equation 3)
Now we can substitute equation 3 into equation 1:
(8/7)(X - 21.5) = (1/4)X + 4
Let's simplify this equation and solve for X:
(8/7)X - (8/7)(21.5) = (1/4)X + 4
(8/7)X - 24.57 = (1/4)X + 4
Multiply both sides of the equation by 28 to eliminate the fractions:
32X - 686.96 = 7X + 112
Combine like terms:
32X - 7X = 112 + 686.96
25X = 798.96
Divide both sides by 25:
X = 31.96
Now that we have the value of X, we can substitute it back into equation 2 to find Y:
Y = (7/8)X + 21.5
Y = (7/8)(31.96) + 21.5
Y = 27.965 + 21.5
Y = 49.465
Therefore, Xena is approximately 31.96 years old and Yuki is approximately 49.465 years old.