For nonzero numbers x,y, and z, 3x=4y and 12y=5z. What is z/x?
from 3x = 4y ---> x = 4y/3
from 12y = 5z --> z = 12y/5
so z/x = (12y/5) / (4y/3)
= (12y/5)(3/4y)
= 9/5
To find the value of z/x, we need to simplify the given equations and solve for z and x individually. Let's start:
From the first equation, we are given that 3x = 4y. We can rearrange this equation to solve for x by dividing both sides by 3, yielding x = 4y/3.
Next, we look at the second equation, which states that 12y = 5z. Similarly, dividing both sides by 12, we get y = 5z/12.
Now that we have expressions for x and y, we can substitute them into each other to find the value of z/x:
x = 4y/3
x = 4(5z/12)/3
Simplifying further:
x = 20z/36
x = 5z/9
Now that we have an expression for x in terms of z, we can substitute this into the equation z/x:
z/x = z/(5z/9)
To divide the numerator by a fraction, we can multiply by its reciprocal, therefore:
z/x = z * (9/5z)
The z cancels out, and we are left with:
z/x = 9/5
So, z/x is equal to 9/5.