Question 1197224

x = 1/4
y = 11/12
z - x = 3/8 * (y-z) = 3/8 * y = 3/8 * z
add 3/8 * z to both sides of the equation to get:
z - x + 3/8 * z = 3/8 * y
add x to both sides of the equation to get:
z + 3/8 * z = 3/8 * y + x
combine like terms to get:
11/8 * z = 3/8 * y + x
since x = 1/4 and y = 11/12, then:
11/8 * z = 3/8 * 11/12 + 1/4 = 33/96 + 24/96 = 57/96
solve for z to get:
z = 57/96 * 8/11 = 456/1056.
y - z = 11/12 - 456/1056 = 968/1056 - 456/1056 = 512/1056 = 16/33.


since the distance from x to z is 3/8 * the distance from z to y, then the distance from x to z = 3/8 * 16/33 = 48/264.
the distance from x to y is therefore 48/264 + 16/33 = 48/264 + 128/264 = 176/264.
y minus x = 11/12 - 1/4 = 11/12 - 3/12 = 8/12 = 176/264.
the two ways of calculating the distance between x and y are the same, confirming the arithmetic was correct.


your solution is that the distance from z to y is equal to 16/33.


let me know if you have any questions.
theo